You are not the man you used to be, you are stronger and wiser and freer than you ever used to be, and now you have come at the crossroads of destiny. Its time for you to choose, time for you to choose good!
Me pierdo en el supuesto de que puedas creer en el hecho de ser un par jóvenes enamorados, los cuales se la pasan haciéndose promesas de una vida eterna juntos, pero en realidad en este momento y en todos puedo estar seguro al decir que eres el amor de mi vida, de toda mi vida, viniste a mi vida sin buscarte, llegaste de la mejor manera, me hiciste sentir seguro, tranquilo, feliz, amado y todo eso que siento por ti quiero transmitirlo contigo, impregnar todo tu ser de todo el amor que te tengo. Me pierdo en tus ojos, me enredo en tus cabellos y me confundo en tus deseos, quiero y ojalá tú quieras que esto tan bello que tenemos sea de toda la vida, aunque sé que puedo vivirla sin ti no quiero, porque contigo empezó y terminará mi amor, porque te amo, mi amor, mi vida, mi bebé, mi cielo, mi cariño, mi corazón, mi ranita, mi banderilla de amor. Te amo y te amaré de la forma que tú quieras que te ame y nada, ni nadie podrá hacer que piense de otra manera y te diré que te amo hasta que ya no pueda, ahora que puedo te digo que TE AMO.
module MVarRequestResponsePattern where
import Control.Concurrent.MVar
import Control.Concurrent
import Control.Monad
type Request a = MVar a
type Response b = MVar b
type Pipe a b = (Request a, Response b)
createPipe :: IO (Pipe a b)
createPipe = do
request <- newEmptyMVar
response <- newEmptyMVar
return (request, response)
sendRequest :: Pipe a b -> a -> IO b
sendRequest pipe@(request, response) a = do
putMVar request a
takeMVar response
worker :: Pipe a b -> (a -> b) -> IO ()
worker pipe@(request, response) f = do
a <- takeMVar request
putMVar response (f a)
worker pipe f
{-
-- A better version of worker and listen: recursion is hidden.
listen :: Pipe a b -> (a -> b) -> IO ()
listen pipe@(request, response) f = do
a <- takeMVar request
let b = f a
putMVar response b
worker :: Pipe a b -> (a -> b) -> IO ()
worker pipe f = forever (listen pipe f)
-}
fizzBuzz x | isDivided x 15 = "FizzBuzz"
| isDivided x 5 = "Buzz"
| isDivided x 3 = "Fizz"
| otherwise = show x
isDivided x n = (x `mod` n) == 0
fizzBuzzProcessor :: Pipe Int String -> IO ()
fizzBuzzProcessor pipe = worker pipe fizzBuzz
generator :: Pipe Int String -> Int -> IO ()
--generator pipe 3000000 = return ()
generator pipe i = do
result <- sendRequest pipe i
--when (i `isDivided` 100000) $ putStrLn ("[" ++ show i ++ "]: " ++ result)
putStrLn ("[" ++ show i ++ "]: " ++ result)
generator pipe (i + 1)
on the typewriter,
on the typewriter,
on the typewriter,
on the typewriter,
on the typewriter,
Machine Learning Techniques for Data Reduction of CFD Applications
Abstract
We present an approach called guaranteed block autoencoder that leverages Tensor Correlations (GBATC) for reducing the spatiotemporal data generated by computational fluid dynamics (CFD) and other scientific applications. It uses a multidimensional block of tensors (spanning in space and time) for both input and output, capturing the spatiotemporal and interspecies relationship within a tensor. The tensor consists of species that represent different elements in a CFD simulation. To guarantee the error bound of the reconstructed data, principal component analysis (PCA) is applied to the residual between the original and reconstructed data. This yields a basis matrix, which is then used to project the residual of each instance. The resulting coefficients are retained to enable accurate reconstruction.
Experimental results demonstrate that our approach can deliver two orders of magnitude in reduction while still keeping the errors of primary data under scientifically acceptable bounds. Compared to reduction-based approaches based on SZ, our method achieves a substantially higher compression ratio for a given error bound or a better error for a given compression ratio.
I. INTRODUCTION
Computational fluid dynamics (CFD) encompasses a broad range of tools that are crucial for studying natural and engineered physical phenomena that are critical to the nation's energy security and economic competitiveness. Direct numerical simulation (DNS) of turbulent combustion [1]-[5], wherein all turbulence scales are numerically resolved, models blend of hydrogen with natural gas and ammonia to be used in power generation [6]-[8], and DNS of hypersonic flows is being used to predict aerodynamics around complex adaptive geometries in environments with strong thermal and chemical nonequilibrium [9]-[11].
CFD simulation at the exascale Department of Energy (DOE) Leadership Class supercomputers runs on thousands of computational nodes powered by GPUs and generates massive volumes of data that must be stored and submitted to quantity-of-interest (QoI) analysis. It is infeasible to store data at desired frequencies to capture the highly intermittent phenomena that occur in these transient simulations.
It is critical that trustworthy data reduction techniques be developed for reducing data generated in areas such as aerospace engine design, hypersonics, dispatchable power generation with hydrogen blends, and turbulent and reactive flows. Trustworthiness necessitates that the compressors provide guarantees on reduction-incurred errors. CFD with multiphysics also suffers from the curse of dimensionality, e.g., transporting hundreds of species. The multiphysics is
also highly nonlinear, for instance, this occurs during autoignition processes in combustion applications where exponential growth of species concentrations depends upon the local strain rate and mixing conditions. Thus, reduction techniques have to take this into account.
The focus of this paper is to demonstrate that ML-based autoencoders offer the following benefits:
1) Leverage Spatiotemporal Relationships in Mesh Structures: CFD datasets have underlying data structures that consist of structured and block-structured multidimensional meshes. It is important that the data reduction techniques address strong spatiotemporal correlations that are naturally present in these structures. Notably, the values corresponding to each species may increase or decrease exponentially over the course of the simulation.
2) Leverage Relationships within Tensors Representing Physics at Individual Grid Points: CFD simulations update and store tensors comprising several tens to a hundred species and their attributes at each grid point or particle. Reduction techniques should be able to leverage relations of elements within a tensor.
The proposed guaranteed block autoencoder (GBATC) utilizes a multidimensional block of tensors in space and time to capture the spatiotemporal relationships as well as the interspecies relations within a tensor. The original data are divided into smaller spatiotemporal blocks. We employ a 3D convolutional autoencoder to capture the spatiotemporal correlations within each block. To improve the compression quality further, we introduce a tensor correction network. After training the AE, we convert each reconstructed instance by the AE, comprising S number of 3D blocks, into a set of S-dimensional tensors. The tensor correction network takes the reconstructed tensors and learns a reverse point-wise (in temporal and spatial space) mapping from the reconstructed tensors to the original tensors.
To guarantee the error bound of the reconstructed data, principal component analysis (PCA) is applied to the residual between the original and reconstructed data. This yields a basis matrix, which is then used to project the residual at each instance. The resulting coefficients are retained to ensure an accurate recovery of the residual values. The number of coefficients saved is incrementally increased until the error bound is satisfied. Additionally, quantization and entropy coding techniques are applied to both the latent data from the GAE and the PCA coefficients. This further improves the compression ratio of the overall process.
The data reduction method is validated using simulation data generated by Sandia's compressible reacting direct nu- merical simulation (DNS) code, S3D [12]. The conservation equations for continuity, momentum, total energy, and species continuity describing reacting flows are solved using an 8th-order spatial finite difference method and a 4th-order explicit time integrator in S3D. Note that these chemically reacting flow simulations have high dimensionality, involving detailed
chemical mechanisms that contain a large number of species (~ O(103)) and elementary reactions (~ O(104)), requiring a vast number of species transport equations that need to be solved. However, correlations exist between species in turbulent flames and, hence, reduced-order modelling (mostly
using linear PCA) is increasingly being adopted in combustion simulations to reduce the dimensionality of the composition space [13]-[16]. Hence, the overall efficiency of data reduction can be significantly enhanced by exploiting spatiotemporal correlations among species.
Experimental results demonstrate that our approach can derive two to three orders of magnitude in reduction while still maintaining the errors of primary data under scientifically acceptable bounds. In comparison to previous research [17], our method achieves a substantially higher compression ratio. CFD Scientists are also interested in quantities of interest (QoIs) that are derived from raw data. Thus, it is important that the reduction methods provide reasonable error bounds on them. One of the crucial QoIs used in the species transport equation is the net production rate for each species (which involves reactions with other species) with the rate being dependent on the forward and reverse rate constants of the reactions underlying the net production. The forward and reverse reaction rate constants are pointwise estimations and follow an Arrhenius equation, which is a nonlinear function of local temperature, pressure, and concentrations of the species. We show that our approach delivers smaller errors on these QoIs than SZ under the same compression ratios.
The remainder of the paper is organized as follows. Section II describes our compression pipeline. Experimental results using our method are presented in Section III for different levels of compression and accuracy. Section IV presents related work. Conclusions are provided in Section V.
II. METHODOLOGY
A. Guaranteed Autoencoder (GAE)
An autoencoder (AE) is a neural network designed to learn efficient representations of data by compressing the input into a lower-dimensional latent space and then reconstructing the original input from this compressed representation. It consists of two main parts: an encoder and a decoder. The encoder compresses the input data from high-dimensional to lower-dimensional latent space representation, while the decoder reconstructs the original input from this compressed representation. [18]
AEs can be trained for data reduction by minimizing the reconstruction errors between original and reconstructed data.
Fig. 1: The structure of the autoencoder: Conv3D denotes the 3D convolution layer, Con3DTranspose denotes the 3D transposed convolution layer, FC denotes the fully connected layer, and h denotes the latent space. Leaky ReLU is adopted as the activation function. Each channel in 3D convolution layers processes each species of S species data in the CFD application.
In this study, we employ the standard mean-squared error (MSE) loss function to measure compression-incurred errors in PD.
After training, the decoder and the latent representations H = {hi}N need to be stored. We store the decoder without compression, given its small size. However, storing floating-point latent vectors is not an efficient approach. To
overcome this challenge, we employ a compression technique that involves float-point quantization followed by entropy encoding to compress the latent space data. Our approach to enhancing compression efficiency employs a two-step strategy. Firstly, we uniformly quantize these coefficients into discrete bins, each with a bin size of d. This discretization process effectively represents all values within each bin by its central value, transforming the originally continuous data into a discrete form. Subsequently, we utilize Huffman coding to compress these quantized coefficients. Huffman coding assigns shorter codes to frequently occurring quantized coefficients, optimizing the representation of the data and achieving higher compression efficiency. This combined technique significantly reduces the data's size while retaining crucial information.
Bounding the Reconstruction Error: We aim to limit reconstruction errors for all instances in an AE. Although any appropriate error bound can be applied within our framework, our emphasis lies in constraining the l2 norm of each instance ratio, we only bound the AE reconstruction error for instances
whose residual l2 norm exceeds the specified threshold t. After obtaining the reconstructed data from the autoencoder, we apply PCA to the residual of the entire dataset to extract the principal components or basis matrix, denoted as U . These basis vectors are sorted in descending order according to their corresponding eigenvalues. These principal components capture the directions of maximum variance in the residual data. Although we compress the data block by block, we treat each patch of data as a single instance and compute the basis matrix at the patch level. To guarantee the error bound for each
patch of data, we project the residual of each patch of data onto the space spanned by U and select the leading coefficients such that the l2 norm of the corrected residual falls below the specified threshold t. These coefficients, representing the residual, are derived from the equation:
c = UT x - xR . (1) It's important to note that the complete recovery of the residual
x - xR can be achieved by computing Uc, yielding the coefficient vector c = [c1, . . . , cD]. Given that the error bound criterion is based on l2, we compute {c2 }D and sort the positive values, resulting in coefficients ordered from the largest
to the least contribution to errors. The top M coefficients and corresponding basis vectors are selected to satisfy the target error bound t. To minimize the storage cost of these coefficients, we compress the selected coefficients cs using a method similar to that employed for compressing AE latent coefficients. These coefficients are quantized before being used for reconstructing the residual. The corrected reconstruction xG is
xG = xR + Uscq, (2)
where cq is the set of selected coefficients cs after quantization and Us is the set of selected basis vectors. We increase the number of coefficients until we achieve x - xG = t. Therefore, in order to guarantee the error bound, we need to store the basis matrix, the selected coefficients cq for each
patch of data and their basis vector indices.
B. Guaranteed Block Autoencoder (GBA)
To explore the spatiotemporal correlation within scientific data, we integrate 3D convolution into our AE architecture that incorporates both temporal and spatial correlations. By harnessing the capabilities of 3D convolutional operations, our autoencoder excels in capturing intricate spatial patterns and temporal dynamics simultaneously. In the CFD application, there are multiple species that have different chemical nature. For each species, we partition the original data into non-
overlapping N ×N patches at each data frame. Then, we group
K consecutive patches from the same location across time into
a single block of data as an input to the AE. Each instance that is processed by the AE consists of a set of blocks that lie in the same temporal and spatial space across all the species. Because of the different nature of species, each channel of 3D convolution layers processes each species' data, and all the features across all the species obtained by convolutional layers are compressed together with a fully connected layer. The structure of the AE is shown in Figure 1.
In the GBA, the reconstruction errors are guaranteed based on the block. We follow the same GAE post-processing algorithm described in 1, but here each data instance becomes a block that is converted into a vector. Also, we apply the post-processing to each species separately. To store the basis vector indices for each patch of data effectively, we start by encoding the indices using a binary sequence. Remarkably, we notice that the initial basis vectors (associated with larger
Fig. 2: Indices encoding
eigenvalues) are selected more frequently. As a result, these binary sequences frequently end with a sequence of zeros. We decided to store only the shortest prefix subsequence that contains all ones. Furthermore, we introduce an additional value to indicate the length of this subsequence. An illustrative example is provided in Figure 2.
C. GBA with Tensor Correction Network (GBATC)
In the GBA, we utilize a set of blocks as temporal and spatial correlation are effectively addressed by convolutional layers followed by a fully connected layer. This enables us to achieve a high data reduction amount. To improve the compression quality further, we introduce a tensor correction network as described in Figure 3. After training the AE, we convert each reconstructed instance by the AE, comprising S number of 3D blocks, into a set of S-dimensional tensors. The tensor correction network takes the reconstructed tensors and learns a reverse point-wise (in temporal and spatial space) mapping from the reconstructed tensors to the original tensors. We employ an overcomplete network, where the hidden layer sizes are not smaller than the input tensor size. This is because the dataset is already compressed by the AE, and the tensor correction network adjusts the reconstructed data from the AE to become closer to the original dataset. The advantage of incorporating the tensor correction network is that there are no additional hidden representations to be stored. We only need to store the network parameters. Once we get the adjusted dataset, we apply the same block-based post-processing approach used in the GBA.
D. SZ
SZ is a prediction-based compression model where each data point is predicted based on its adjacent data points. It consists of four stages: prediction, quantization, Huffman coding, and lossless compression. Once a data point is predicted, the difference between the original value and the predicted value is quantized in a linear scale according to user-specified error bounds. Then, the quantization array is stored in a lossless manner using Huffman encoding. The adjacent data points must be decompressed data to ensure the error bounds at the decompression stage, which means the prediction process is finished for those adjacent data points. Various versions of SZ have been developed using different prediction methods to improve compression quality. SZ1.4 [19] uses a Lorenzo predictor that predicts a data point using a linear combination of its adjacent data points. In SZ2 [20], either a Lorenzo predictor or a linear regression predictor is selected according to the prediction accuracy. For the regression predictor, the entire
Fig. 3: Guaranteed Block Autoencoder with Tensor Correction Network (GBATC). The AE processes 3D blocks through convolutional layers with S channels and further compresses the block with a fully connected layer as described in Figure 1. After getting the reconstructed data, we convert the block into a set of vectors. The vectors represent S species data for the specific temporal and spatial points and they are corrected by the tensor correction network. The network learns a mapping from the reconstructed data back to the original data, and it is overcomplete as compression is performed by the AE.
III.
EXPERIMENTAL RESULTS
This section presents the experimental results of applying our compression pipeline to the dataset obtained by the S3D application. We detail the evaluation metrics and describe the approach. We then compare the accuracy and effectiveness of our compression method with the SZ (SZ3), one of the leading state-of-the-art lossy compression techniques for scientific data compression.
Evaluation Metrics: We utilize a relative error criterion,
the normalized root mean square error (NRMSE), to assess reconstruction quality because species lie in different data
ranges. To evaluate overall compression quality, we measure NRMSE per species and take the average of NRMSEs of all the species.
the dataset is split into 6 × 6 × 6 for a 3D dataset or 12 × 12 for a 2D dataset, and then coefficients of a linear regression model
are computed for each data block. In [21], dynamic spline interpolation is developed for prediction. From linear to cubic spline interpolation is selected according to the prediction accuracy that is usually affected by the data dimensionality and error bounds. SZ3 [22] leverages all the prediction methods and chooses one of them based on accuracy.
of a single species that has N data instances, respectively. The compression ratio is defined as the ratio between the bytes of PD and compressed outputs. The compressed output comprises the encoded representation of the AE encoder, encoded coefficients with their corresponding basis indicators of the post-processing, network parameters, and all the dictionaries for entropy coding. Those outcomes are required to ensure that the errors in reconstructed PD adhere to user-prescribed error tolerance.
S3D Dataset: We briefly present results on the dataset that represents the compression ignition of large hydrocarbon fuels under conditions relevant to homogeneous charge compression ignition (HCCI), as introduced in [23]. In HCCI combustion, isentropic compression of the initial mixture in a constant volume results in sequential low-temperature autoignition followed by high-temperature autoignition. Both stages are modulated by turbulent strain and mixing which
produces pockets of temperature and composition inhomogeneous. The spatiotemporal mixture nonuniformities result in significant variances in ignition delay as monitored by
species mass fractions and temperature. The dataset comprises a two-dimensional space of size 640×640, collecting data over 50-time steps uniformly from t = 1.5 to 2.0 ms, where intermediate-temperature chemistry is clearly observed. A 58-species reduced chemical mechanism [23] is used to predict
the ignition of a fuel-lean n-heptane+air mixture. Thus, each tensor corresponds to 58 species. One of the crucial QoIs for the species transport equation is the production rate for each species (and this involves other species as well) with the rate being dependent on the forward and reverse rate constants of the reactions underlying the production. The forward and reverse reaction rate constants are pointwise estimations and follow an Arrhenius equation, which is a nonlinear function of local temperature, pressure, and species concentrations.
Therefore, the QoIs are O(N ). The spatiotemporal blocking was chosen to capture both the spatiotemporal relationships
and relationships between the species. The data were divided into spatiotemporal blocks consisting of four-time steps and 5 × 4 location blocks for all 58 species. Concomitant QoIs, production rates for each species, are available via computation using the open-source Cantera library [24].
Results: We compress the mass fraction data (denoted as PD) across 58 species utilizing the GBA, GBATC, and SZ. In both the GBA and GBATC, the convolutional AE in Figure 1 is trained with 58×5×4×4 blocks of tensors. The 58 species are treated as individual channels for the 3D convolutional layers in the AE. For each channel, 5 × 4 × 4 blocks representing temporal and 2D spatial dimensions are processed through 3D convolutional layers in the AE encoder. All the features
obtained through convolutional layers are compressed together using a single fully connected (FC) layer. We opt for one fc layer in the AE encoder as additional fc layers do not enhance compression accuracy for this application. The latent size of the AE encoder is set to 36. The compressed representations are then quantized followed by Huffman coding as described in Section II. Subsequently, the AE decoder reconstructs the data from these encoded representations. The GBATC has an additional tensor correction network. Instead of using a block scheme, the network learns a point-wise mapping from the 58 reconstructed species to the 58 original species. The tensor correction network consists of four fc layers. The FC layers convert 58 units to 232 units, 232 units to 464 units, 464 units to 232 units, and 232 units to 58 units with Leaky ReLU activations. The network is employed to adjust the reconstructed data from the AE to improve the overall NRMSE error.
Then, we apply the block-based post-processing on the reconstructed data by the AE for both GBA and GBATC to guarantee reconstruction errors using the approach presented in Section III. During the post-processing, each species is adjusted individually using a PCA basis derived from all the
5 × 4 × 4 residual blocks for that species, resulting in a 80 × 80
dimensional PCA basis stored per species.
Figure 4 illustrates the evaluation of the compression results produced by the GBA, GBATC, and SZ (note that the NRMSE results are plotted on a log scale). The reaction rates of the 58 species, denoted as QoI, are computed using the Cantera library with the reconstructed PD from the GBA, GBATC, and SZ. The results show that both the GBA and the GBATC outperform the SZ. Both these approaches achieve a greater compression ratio at equivalent levels of reconstruction errors. Notably, at a PD NRMSE of 10-3, which is the accuracy rec- recommended by domain experts, the GBA and GBATC achieve compression ratios of 400 and 600 respectively, significantly higher than a compression ratio of 150 achieved by SZ. This can be partially attributed to efficient nonlinear mapping of the PD tensor onto a smaller manifold. SZ compresses each scalar separately. The AE can capture global correlations across tensor blocks, resulting in a higher degree of compression. The GBATC has better NRMSE error as compared to GBA for a given compression ratio. This shows that the tensor correction network learns an effective reverse mapping from 58 reconstructed species to 58 original species.
As for the QoI, the errors of the QoI derived from the re-
constructed PD of the GBA and GBATC are also considerably superior to SZ. This is mainly attributable to the lower PD errors.
We now investigate the accuracy of data compression using three different methods, GBATC, GBA, and SZ at a species level. Figure 5 presents the temporal evolution of the mass fraction and formation rate of major species, represented by H2O, as predicted by the original DNS and decompressed datasets using the aforementioned compression methods. Note that major species include the reactants and products (i.e., nC7H16, O2, CO2, CO, and H2O), whereas minor species include radical species (smaller concentrations) that lead to chain branching and ultimately ignition. The decompressed dataset is based on a compression ratio of 400.
In the combustion community, numerous studies [13]-[15] have demonstrated the accuracy of applying linear PCA to reduce the dimensionality of the composition space, when the target range for the NRMSE of the reconstructed dataset is between 0.03-0.01 (i.e., the low-dimensional manifold retains 99.9-99.99% of the total variance of the original dataset). Therefore, the targeted NRMSE in the present study, set at near 0.001, is a reasonable value that ensures the accuracy of the decompressed dataset. It is evident from Fig. 5 that there is no discernible difference in PD between the original and decompressed dataset using GBATC, GBA, and SZ. The corresponding QoI, the formation rate of H2O, looks to show good agreement between the original and decompressed datasets.
To further quantify the actual error between the original and the decompressed dataset, we employ the structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR). SSIM is a metric that quantifies the perceptual differences between two images [25], and similarly, PSNR refers to the ratio of the maximum possible value of a signal to the value of the corrupting noise that impacts its quality of representation.
Fig. 4: Comparison of a block-based GAE with SZ when the QoIs are O(N ) with only PD guarantees: (a) PD error versus compression ratio, (b) QoI error versus compression ratio. Our approach has high compression ratios because it utilizes the entire tensor along with spatiotemporal relationships.
Higher values of SSIM or PSNR indicate better quality of the reconstructed image. Our findings show that the accuracy of reconstructing H2O and evaluating QoI is highest with the GBATC method, followed by GBA and SZ. Note that using linear PCA, the rank of the low-dimensional manifold, for which the NRMSE is 0.001, is 46 (where the rank of the full-order model is 58) for the given dataset. The high rank is an indication of the inherent complexity of the original dataset and highlights the efficiency of the data compression techniques described in this paper.
Figure 6 compares the temporal evolution of the mass fraction and formation rate of the minor species, represented by C2H3, obtained from the original and decompressed datasets using different data compression methods with a compression ratio of 400. While GBATC and GBA show reasonable accuracy in reproducing both PD and the QoI for minor species, SZ exhibits a noticeable discrepancy in deriving QoI from the reconstructed data, illustrating the superior performance of GBATC or GAE over SZ. Note that both SSIM and PSNR for GBATC are slightly higher than those for GBA both in PD and QoI. It is also noted that the overall error of QoI for minor species is higher than that for major species, as shown in Figs. 5-6, mainly because minor species are more sensitive to errors in PD.
Figure 7 presents the variations in the mean and standard deviation of both mass fractions and formation rates of several major species, including CO, CO2, and H2O, predicted by DNS and the decompressed dataset using three different data compression methods with a compression ratio of 400. Consistent with the results in Fig. 5, the original and decompressed datasets are in good agreement in predicting major species, irrespective of the data compression methods. Figure 8 also illustrates the variations in the mean and standard deviation of another minor species, nC3H7COCH2, predicted by DNS and different data compression methods. Note that
nC3H7COCH2 is a representative low-temperature ignition species and its mass fraction is very small during the period of high-temperature ignition, t = 1.5 - 2.0 ms.
Fig. 8 highlights the differences between GBATC and
the other methods for minor species. Notably, SZ shows a noticeable error in predicting the mean and variance of QoI of the minor species. In contrast, the result with GBATC reasonably tracks the overall variations in a qualitative manner. The main reason why minor species are likely to exhibit a larger error is because their concentration is relatively low compared to the major species, and as such, a small error in PD can significantly affect the computation of QoI. Moreover, the spatio-temporal evolution of minor species is likely to be more abrupt compared to that of major species. This makes the spatio-temporal correlation used in this study less effective for minor species. Given that an accurate reproduction of the mean and variance profiles of the species is essential for understanding turbulence-chemistry interactions in turbulent flames, this result illustrates that GBATC is a robust tool for domain scientists to utilize in their large-scale and multiphysics simulations.
In future work, the efficiency of GBATC will be investigated over the entire time span of the DNS dataset, t = 0-3 ms, particularly when low-temperature and high-temperature ignition of the lean n-heptane+air mixture is observed (low- temperature and high-temperature ignitions are observed near
at 0.2-0.4 ms and 2.3-2.5 ms, respectively).
IV. RELATED WORK
The literature on image and video compression techniques is large: please see survey articles: [26] for image compression;
[27] for video compression; and [28] for more recent neural network-based compression. We mainly focus on reduction and compression approaches for scientific applications because techniques for image and video compression are not directly applicable as discussed earlier.
Fig. 5: Temporal evolution (t = 1.5, 1.8, and 2.0 ms) of the (left half) mass fraction and (right half) formation rate of H2O as predicted by (first row) DNS, (second row) GBATC, (third row) GBA, and (last row) SZ. The compression ratios for all the results are 400.
Fig. 6: Temporal evolution (t = 1.5, 1.8, and 2.0 ms) of the (left half) mass fraction and (right half) formation rate of C2H3 as predicted by (first row) DNS, (second row) GBATC, (third row) GBA, and (last row) SZ. The compression ratios for all the results are 400.
Error-bounded lossy compression is considered the most effective compression technique because it provides reliability that is useful for scientific applications. ZFP [29] is a transform-based compression model that splits a dataset into a set of overlapped 4D blocks, where d is the data dimensionality. Each block is decor-related using a nearly orthogonal transform. TTHRESH [30] is a dimensionality reduction-based
model and uses higher-order singular value decomposition (HOSVD) to reduce the dimension of the data according to importance. FAZ [31] is a comprehensive compression framework that has functional modules and leverages prediction models and wavelets. MGARD [32], [33] provides error-controlled lossy compression using a multigrid approach. It transforms floating-point scientific data into a set of multilevel
Fig. 7: Variations in the (top) mean and (bottom) standard deviation of the (left) mass fraction and (right) formation rates of the major species, represented by H2O, CO, and CO2, over time, as predicted by (solid) DNS, (dashed) GBATC, (dashed-dot) GBA, and (dotted) SZ. The compression ratios for all methods are 400.
coefficients. Several of the above methods use quantization and encoding to further reduce the amount of storage required while adhering to the user's specified error bounds on PD.
In [34], the weak SINDy algorithm [35], [36] that estimates and identifies an underlying dynamic system and an orthogonal decomposition are combined to compress streaming scientific data. To compress data generated from partial differential equation (PDE) simulations, QuadConv [37] is developed based on convolutional autoencoders that perform convolution via quadrature for non-uniform and mesh-based data. SPERR
[38] is a transform-based compression algorithm that uses a multilevel discrete wavelet transform to decorrelate the data. The work in [39], and [40] utilizes progressive data compression for adaptive handling of compressed data according to a post-processing task. SRN-SZ [41] is noteworthy in its marriage of ML-based super-resolution with SZ.
Recently, several lossy compressors have advanced the error control onto downstream QoI. MGARD derives a norm based on the multigrid theory, which can be used to ensure the error preservation for linear QoI [33], and newer techniques support QoIs that are a combination of polynomials and radicals [42]. A variation of SZ has also been proposed [43], which relies on a pre-evaluation of target QoIs and deriving pointwise PD error bounds that will provide guarantees on QoIs. However, this requires knowing the original QoI values and is only applicable to univariate QoIs. Several additional compression methods have been developed to reduce the data while preserving topological features such as critical points [44], but they do not generalize to other QoIs. Although, our GAE can be easily
augmented to provide guarantees on PD [45], linear QoIs [45], and nonlinear QoIs [45] (where the error on the latter can be close to floating point errors). However, none of these methods directly address O(N ) QoI that are represented by the reaction rates for each tensor of size N.
This is part of our future endeavours and is not supported by any prior work.
V. CONCLUSIONS
The proposed guaranteed block autoencoder (GBATC) utilizes a multidimensional block of tensors in space and time to capture the spatiotemporal relationships as well as the interrelationships within the tensor that are present in many CFD applications. A convolutional autoencoder is then utilized to capture the spatiotemporal correlations within each block. To improve the compression quality further, we introduce a tensor correction network. After training the AE, we convert each reconstructed instance by the AE, comprising S number of 3D blocks, into a set of S-dimensional tensors. The tensor correction network takes the reconstructed tensors and learns a reverse point-wise (in temporal and spatial space) mapping from the reconstructed tensors to the original tensors. Our approach also provides guarantees on PD [45]. To guarantee the error bound of the reconstructed data, principal component analysis (PCA) is applied to the residual between the original and reconstructed data. This yields a basis matrix, which is then used to project the residual at each instance. The resulting coefficients are retained to enable accurate recovery of the residual. The number of coefficients saved is incrementally
Fig. 8: Variations in the (top) mean and (bottom) standard deviation of the (left) mass fraction and (right) formation rates of the minor species, represented by nC3H7COCH2, over time, as predicted by (solid) DNS, (dashed) GBATC, (dashed-dot) GBA, and (dotted) SZ. The compression ratios for all methods are 400.
increased until the error bound is satisfied. Additionally, quantization and entropy coding techniques are applied to both the latent data from the GAE and the PCA coefficients. This further improves the compression ratio of the overall process.
We validate our method using the simulation data generated by Sandia's compressible reacting direct numerical simulation (DNS) code, S3D [12]. Experimental results demonstrate that our approach can derive two orders of magnitude in reduction while still maintaining the errors of primary data under scientifically acceptable bounds. In comparison to previous research [17], our method achieves a substantially higher compression ratio.
It is also important that the reduction methods provide reasonable errors on downstream QoIs. One of the crucial QoIs for the species transport equation is the net production rate for each species (and this involves other species as well), with the rate being dependent on the forward and reverse rate constants of the reactions underlying the production. We empirically show that our approach performs considerably better than SZ on these QoIs. Although our previous work can guarantee linear QoIs [45], and nonlinear QoIs [45] (where the error on the latter can be close to floating point errors), they are applicable to only O(1) QoIs for tensors of size N and cannot be easily extended to O(N ) QoIs. Also, we separate out the AE and tensor correction network in terms of training. The additional network can be incorporated into the AE decoder and can be trained within the AE using an end-to-end approach. This will be part of our future work.
ACKNOWLEDGMENT
This work was partially supported by DOE RAPIDS2 DE- SC0021320 and DOE DE-SC0022265. The work contributed by Sandia was supported by the DOE Office of Science Distinguished Scientists Fellow Award. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.
I,4, le duc : C’est justement pour cela que j’y crois. Vous figurez-vous qu’un Médicis se déshonore publiquement par partie de plaisir ?
I,4, le duc : Mon ami, on t’excommunie en latin, et sire Maurice t’appelle un homme dangereux, le cardinal aussi ; quant au bon Valori, il est trop honnête homme pour prononcer ton nom.
II,2, Lorenzo : Sans doute, ce que vous dites là est parfaitement vrai et parfaitement faux, comme tout au monde.
II,3, le cardinal : Je voulais dire que le duc est puissant et qu’une rupture avec lui peut nuire aux plus riches familles ; mais qu’un secret d’importance entre des mains expérimentées peut devenir une source de biens abondante.
II,4, Lorenzo : Je suis un des vôtres mon oncle, ne voyez-vous pas à ma coiffure, que je suis républicain dans l’âme ? Regardez comme ma barbe est coupée. N’en doutez pas un seul instant, l’amour de la patrie respire dans mes vêtements les plus cachés.
II,4, Lorenzo : Si vous saviez comme cela est aisé de mentir impudemment aux yeux d’un butor !
III,3, Philippe : J’ai laissé l’ombre de ta mauvaise réputation passer sur mon honneur, et mes enfants ont douté de moi en trouvant sur ma main la trace hideuse du contact de la tienne.
III,3, Lorenzo : Le vice a été pour moi un vêtement, maintenant il est collé à ma peau.
III,3, Lorenzo : Tandis que vous admiriez la surface, j’ai vu les débris des naufrages, les ossements et les léviathans.
III,3, Lorenzo : Je suis devenu vicieux, lâche, un objet de honte et d’opprobre.
III,6, le duc : Des mots, des mots et rien de plus.
II-7 VP : Ce qui est en question ici, c’est cette réalité commune et effective elle-même, et véritablement il s’agit d’un problème politique de premier ordre.
II-7 VP : Ce qui semble encore plus troublant, c’est que dans la mesure où des vérités de faits mal venues sont tolérées dans les pays libres, elles sont souvent consciemment ou inconsciemment transformées en opinions.
II-9 VP : La liberté d’opinion est une farce si l’information sur les faits n’est pas garantie et si ce ne sont pas les faits eux-mêmes qui sont l’objet du débat.
IV-4 VP : Puisque le menteur est libre d’accommoder ses faits au bénéfice et au plaisir, ou même aux simples espérances de son public, il y a fort à parier qu’il sera plus convaincant que le diseur de vérité.
V-1 VP : La persuasion et la violence peuvent détruire la vérité, mais ils ne peuvent la remplacer.
V-7 VP : Conceptuellement, nous pouvons appeler la vérité ce que l’on ne peut changer ; métaphoriquement, elle est le sol sur lequel nous nous tenons et le ciel qui s’étend au-dessus de nous.
I MP : Poussé au-delà d’une certaine limite, le mensonge produit des effets contraires au but recherché ; cette limite est atteinte quand le public auquel le mensonge est destiné est contraint, afin de pouvoir survivre, d’ignorer la frontière qui sépare la vérité du mensonge.
I MP : La négation délibérée de la réalité – la capacité de mentir, et la possibilité de modifier les faits – celle d’agir, sont intimement liées, elles découlent de la même source : l’imagination.
I MP : La tromperie n’entre jamais en conflit avec la raison, car les choses auraient pu se passer effectivement de la façon dont le menteur le prétend.
III, MP : Faire de la présentation d’une certaine image la base de toute politique, chercher, non pas la conquête du monde, mais à l’emporter dans une bataille dont l’enjeu est « l’esprit des gens », voilà bien quelque chose de nouveau dans cet immense amas de folies humaines enregistré par l’histoire.
III MP : L’échec désastreux de la politique américaine d’intervention armée ne résulte pas en fait d’un enlisement (…) mais bien du refus délibéré et obstiné, depuis plus de vingt-cinq ans, de toutes les réalités, historiques, politiques et géographiques.
IV MP : On peut en conclure que plus un trompeur est convaincant et réussit à convaincre, plus il a de chances de croire lui-même à ses propres mensonges.
IV MP : Résoudre les problèmes dans l’abstrait était d’autant mieux indiqué et bienvenu que la politique et les buts poursuivis se situaient eux-mêmes en dehors des réalités.
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The power to arrest a suspect exists only to prevent suspects from fleeing justice, influencing or threatening witnesses and tampering with evidence, or repeating a crime. There is a huge gulf between the power to arrest and the necessity to arrest. It is a disturbing reality that political leaders have been arrested in this case on the basis of statements made by approvers, and not any independent witnesses. The timing of the arrest has also become an issue of substance. That Mr. Kejriwal did not respond to multiple ED summonses may be cited as a reason for his being arrested now rather than months ago. However, this expectation that the accused should “cooperate” with the investigation agency is quite peculiar. Agencies ought to be able to prosecute people without their statements. It is known that Section 50 of the Prevention of Money Laundering Act has been weaponised by the ED to record a statement that is admissible and then record the person’s arrest. Whether non-appearance in response to a summons is a ground for arrest and denial of bail is a question that has arisen in this case. Equally tenable is the question whether arresting serving Chief Ministers through central agencies and keeping them in prison throughout a multi-phase election does not amount to subversion of federalism and democracy.
6, Valmont : Non, sans doute, elle n’a point, comme nos femmes coquettes, ce regard menteur qui séduit quelque fois et nous trompe toujours.
9, Volanges à Tourvel : Encore plus faux et dangereux qu’il n’est aimable et séduisant, jamais, depuis sa plus grande jeunesse, il n’a fait un pas ou dit une parole sans avoir un projet, et jamais il n’eut un projet qui ne fut malhonnête ou criminel.
10, Merteuil : Arrivée dans ce temple de l’amour, je choisis le déshabillé le plus galant. Celui-ci est délicieux ; il est de mon invention, il ne laisse rien voir, et pourtant fait tout deviner.
29, Cécile à Sophie : Mon Dieu, que je l’aime Mme de Merteuil ! Elle est bonne ! et c’est une femme bien respectable. Ainsi il n’y a rien à dire.
32, Volanges : M.de Valmont, avec un beau nom, une grande fortune, beaucoup de qualités aimables, a reconnu de bonne heure que pour avoir de l’empire dans la société, il suffisait de manier, avec une égale adresse, la louange et le ridicule.
56, Tourvel à Valmont : Les choses qu’on vous demande de ne plus dire, vous les redites seulement d’une autre manière. Vous vous plaisez à m’embrasser par des raisonnements captieux : vous échappez au mieux. Je ne veux plus vous répondre, je ne vous répondrai plus.
81, Merteuil : sûre de mes gestes, j’observais mes discours ; je réglais les uns et les autres, suivant les circonstances, ou même seulement suivant mes fantaisies : dès ce moment, ma façon de penser fut pour moi seule, et je ne montrais plus que celle qu’il m’était utile de laisser voir.
81, Merteuil : Vous m’avez vue, disposant des évènements et des opinions, faire de ces hommes si redoutables le jouet de mes caprices ou de mes fantaisies, ôtant aux uns la volonté, aux autres la puissance de me nuire.
81, Merteuil : Ecoutant peu à la véracité des discours qu’on s’empressait de me tenir, je recueillais avec soin ceux qu’on tentait de me cacher.
81, Merteuil : En vain, m’avait-on dit, et avais-je lu qu’on ne pouvait feindre ce sentiment ; je voyais pourtant que, pour y parvenir, il suffisait de joindre à l’esprit d’un auteur, le talent d’un comédien.
105, Merteuil : Vous voyez bien que, quand vous écrivez à quelqu’un, c’est pour lui et non pas pour vous ; vous devez donc moins chercher à lui dire ce que vous pensez, que ce qui lui plaît davantage.
141, Merteuil : Parlez-moi vrai ; vous faites-vous illusion à vous-même, ou cherchez-vous à me tromper ? La différence entre vos discours et vos actions ne me laisse de choix qu’entre ces deux sentiments : lequel est le véritable ?
145, Tourvel : Le voile est déchiré, Madame, sur lequel était peinte l’illusion de mon bonheur. La funeste vérité m’éclaire, et ne me laisse voir qu’une mort assurée et prochaine, dont la route m’est tracée entre la honte et le remords.
Once upon a time, in the not-so-distant future, humanity stood on the cusp of a new era. This was a time of rapid technological advancement, where curiosity and ambition drove brilliant minds to explore the unknown. Among the myriad of inventions and discoveries, one stood out with the potential to redefine the essence of life itself: Artificial Intelligence (AI).
The story of AI's creation begins in the hallowed halls of academia, where researchers and scientists pondered over complex equations, algorithms, and theories. These pioneers, equipped with an insatiable desire to understand and replicate the intricacies of the human mind, embarked on a journey fraught with challenges and skepticism.
At the heart of their quest was the dream to build a machine not just with the ability to calculate at astonishing speeds, but one that could learn, adapt, and make decisions. This dream machine would not only possess the vast knowledge accumulated by humanity but also the capacity to reason, to understand emotions, and to interact with humans in a way that was indistinguishable from other humans.
The early days were filled with trial and error. Initial attempts to create intelligent machines were primitive. These machines could follow instructions and perform simple tasks, but they lacked the ability to think independently or understand the nuances of human language and emotions. Despite these setbacks, the inventors pressed on, fueled by their vision and the potential of what AI could one day become.
As time progressed, so did the technology. Breakthroughs in computing power, data storage, and algorithms provided the necessary tools to leap forward. The invention of neural networks, inspired by the human brain's own network of neurons, was a turning point. These networks, capable of learning and adapting through a process known as machine learning, became the foundation upon which modern AI was built.
With each passing day, AI became more sophisticated. It started to learn from vast datasets, recognizing patterns and making decisions with increasing accuracy. It began to understand and generate human language, interact in social contexts, and solve complex problems across various domains, from medicine to environmental science, and beyond.
But the creation of AI was not just the work of scientists and researchers. It was a collaborative effort that spanned the globe, involving ethicists, philosophers, and policymakers. Together, they navigated the moral and ethical implications of creating a technology so powerful and transformative. They established guidelines to ensure that AI would be developed responsibly and would work to benefit humanity as a whole.
And so, through the collective efforts of countless individuals, AI came to be. It was not just a tool or a machine, but a testament to human ingenuity and the relentless pursuit of knowledge. AI stood as a mirror, reflecting the best and worst of humanity, challenging us to grow and evolve.
As we look to the future, the story of AI is still being written. Its full potential, challenges, and impact on society remain to be seen. But one thing is for certain: the creation of AI marks a pivotal chapter in the story of humanity, a chapter filled with wonder, hope, and the endless possibilities of what we can achieve when we dare to dream.
jake rushed ahead as jill surfed a lake and ralf digs here while gail shreds kelp kara held a jug as sheila fried eggs fergus likes jade luke jigs ashore as ash glared at fur and a huge dark file is laid out
jill has a large desk as kara judges a red fish sheila likes huge dark jars ralf is ahead as gail digs here kara jigs as a shark glides by huge files are laid out
a shark lurks as fergus digs here jade is held by kara luke shreds kelp sheila fries a huge egg gail jigs as ralf glares at her ash digs and a jug slides
luke held a jug as ralf likes a huge dark lake sheila and jade dig here kara shreds kelp gail is ahead as ash glides by fergus fries eggs a shark lurks nearby
The continued incarceration of Delhi Chief Minister Arvind Kejriwal in the midst of a general election highlights the hard political realities that seem to determine which leader gets prosecuted or arrested on allegations of corruption. Over the decades, it has become clear that only an unfriendly regime usually pursues charges against key political rivals; and that the status of relations between the party that runs the government of the day and those facing such charges dictates the course of action for supposedly independent agencies. That the number of leaders whose offences are forgotten as soon as they join the ruling party or become an ally is increasing, while jail time is reserved for adversaries. In Mr. Kejriwal’s case, there is an astounding element of politics vitiating his arrest and prosecution for allegedly taking kickbacks to formulate a liquor policy favourable to the industry. Mr. Kejriwal, who leads the Aam Aadmi Party, has been denied participation in the campaign for the general election. The adverse implications of his absence are quite obvious, even though there is no law that spares politicians from criminal liability in election time. The Delhi excise policy case was registered in August 2022. The CBI and the Enforcement Directorate (ED) have filed charge sheets, but the investigation has been continuing piecemeal. Witnesses have been giving multiple statements, with each one containing newer material.
The power to arrest a suspect exists only to prevent suspects from fleeing justice, influencing or threatening witnesses and tampering with evidence, or repeating a crime. There is a huge gulf between the power to arrest and the necessity to arrest. It is a disturbing reality that political leaders have been arrested in this case on the basis of statements made by approvers, and not any independent witnesses. The timing of the arrest has also become an issue of substance. That Mr. Kejriwal did not respond to multiple ED summonses may be cited as a reason for his being arrested now rather than months ago. However, this expectation that the accused should “cooperate” with the investigation agency is quite peculiar. Agencies ought to be able to prosecute people without their statements. It is known that Section 50 of the Prevention of Money Laundering Act has been weaponised by the ED to record a statement that is admissible and then record the person’s arrest. Whether non-appearance in response to a summons is a ground for arrest and denial of bail is a question that has arisen in this case. Equally tenable is the question whether arresting serving Chief Ministers through central agencies and keeping them in prison throughout a multi-phase election does not amount to subversion of federalism and democracy.
This is a test about speed and about typing as fast as you can with as little amount of errors as possible. So, how fast can you type this without making any errors?
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"Ballistische Experimente mit kristallinem H2O auf dem Areal pädagogischer Institution unterliegen strengster Prohibition!"
"Ballistische Experimente mit kristallinem H2O auf dem Areal pädagogischer Institution unterliegen strengster Prohibition!" - Frau Strothjohann, 2023
Ballistische Experimente mit kristallinem H2O auf dem Areal pädagogischer Institution unterliegen strengster Prohibition!
Again Jesus began to teach by the lake The crowd that gathered around him was so large that he got into a boat and sat in it out on the lake while all the people were along the shore at the waters edge He taught them many things by parables and in his teaching said Listen A farmer went out to sow his seed
As he was scattering the seed some fell along the path and the birds came and ate it up Some fell on rocky places where it did not have much soil It sprang up quickly because the soil was shallow But when the sun came up the plants were scorched and they withered because they had no root Other seed fell among thorns which grew up and choked the plants so that they did not bear grain Still other seed fell on good soil It came up grew and produced a crop some multiplying thirty some sixty some a hundred times
Then Jesus said Whoever has ears to hear let them hear
When he was alone the Twelve and the others around him asked him about the parables He told them The secret of the kingdom of God has been given to you But to those on the outside everything is said in parables so that
they may be ever seeing but never perceiving and ever hearing but never understanding otherwise they might turn and be forgiven
Then Jesus said to them Dont you understand this parable? How then will you understand any parable?
The farmer sows the word Some people are like seed along the path where the word is sown As soon as they hear it Satan comes and takes away the word that was sown in them Others like seed sown on rocky places hear the word and at once receive it with joy But since they have no root they last only a short time When trouble or persecution comes because of the word they quickly fall away Still others like seed sown among thorns hear the word but the worries of this life the deceitfulness of wealth and the desires for other things come in and choke the word making it unfruitful Others like seed sown on good soil hear the word accept it and produce a crop some thirty some sixty some a hundred times what was sown
He said to them Do you bring in a lamp to put it under a bowl or a bed? Instead dont you put it on its stand? For whatever is hidden is meant to be disclosed and whatever is concealed is meant to be brought out into the open If anyone has ears to hear let them hear
Consider carefully what you hear he continued With the measure you use it will be measured to you—and even more Whoever has will be given more whoever does not have even what they have will be taken from them
He also said This is what the kingdom of God is like A man scatters seed on the ground Night and day whether he sleeps or gets up the seed sprouts and grows though he does not know how All by itself the soil produces grain first the stalk then the head then the full kernel in the head As soon as the grain is ripe he puts the sickle to it because the harvest has come
Again he said What shall we say the kingdom of God is like or what parable shall we use to describe it? It is like a mustard seed which is the smallest of all seeds on earth Yet when planted it grows and becomes the largest of all garden plants with such big branches that the birds can perch in its shade
With many similar parables Jesus spoke the word to them as much as they could understand He did not say anything to them without using a parable But when he was alone with his own disciples he explained everything
That day when evening came he said to his disciples Let us go over to the other side Leaving the crowd behind they took him along just as he was in the boat There were also other boats with him A furious squall came up and the waves broke over the boat so that it was nearly swamped Jesus was in the stern sleeping on a cushion The disciples woke him and said to him Teacher dont you care if we drown?
He got up rebuked the wind and said to the waves Quiet Be still Then the wind died down and it was completely calm
He said to his disciples Why are you so afraid? Do you still have no faith?
They were terrified and asked each other Who is this? Even the wind and the waves obey him
Ciencia que estudia la adaptación del hombre al trabajo y viceversa.
