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Data compression plays a key role in reducing storage and I/O costs. Traditional lossy methods primarily target data on rectilinear grids and cannot leverage the spatial coherence in unstructured mesh data, leading to suboptimal compression ratios. We present a multi-component, error-bounded compression framework designed to enhance the compression of floating-point unstructured mesh data, which is common in scientific applications. Our approach involves interpolating mesh data onto a rectilinear grid and then separately compressing the grid interpolation and the interpolation residuals. This method is general, independent of mesh types and typologies, and can be seamlessly integrated with existing lossy compressors for improved performance. We evaluated our framework across twelve variables from two synthetic datasets and two real-world simulation datasets. The results indicate that the multi-component framework consistently outperforms state-of-the-art lossy compressors on unstructured data, achieving, on average, a $2.3-3.5\times$ improvement in compression ratios, with error bounds ranging from $\num{1e-6}$ to $\num{1e-2}$. We further investigate the impact of hyperparameters, such as grid spacing and error allocation, to deliver optimal compression ratios in diverse datasets., Comment: 10 pages, 9 figures. 2024 IEEE 20th International Conference on e-Science (e-Science). IEEE, 2024

This article introduces a novel family of optimization algorithms - Anisotropic Gaussian Smoothing Gradient Descent (AGS-GD), AGS-Stochastic Gradient Descent (AGS-SGD), and AGS-Adam - that employ anisotropic Gaussian smoothing to enhance traditional gradient-based methods, including GD, SGD, and Adam. The primary goal of these approaches is to address the challenge of optimization methods becoming trapped in suboptimal local minima by replacing the standard gradient with a non-local gradient derived from averaging function values using anisotropic Gaussian smoothing. Unlike isotropic Gaussian smoothing (IGS), AGS adapts the smoothing directionality based on the properties of the underlying function, aligning better with complex loss landscapes and improving convergence. The anisotropy is computed by adjusting the covariance matrix of the Gaussian distribution, allowing for directional smoothing tailored to the gradient's behavior. This technique mitigates the impact of minor fluctuations, enabling the algorithms to approach global minima more effectively. We provide detailed convergence analyses that extend the results from both the original (unsmoothed) methods and the IGS case to the more general anisotropic smoothing, applicable to both convex and non-convex, L-smooth functions. In the stochastic setting, these algorithms converge to a noisy ball, with its size determined by the smoothing parameters. The article also outlines the theoretical benefits of anisotropic smoothing and details its practical implementation using Monte Carlo estimation, aligning with established zero-order optimization techniques., Comment: 32 pages, 2 figures

We present a general framework for compressing unstructured scientific data with known local connectivity. A common application is simulation data defined on arbitrary finite element meshes. The framework employs a greedy topology preserving reordering of original nodes which allows for seamless integration into existing data processing pipelines. This reordering process depends solely on mesh connectivity and can be performed offline for optimal efficiency. However, the algorithm's greedy nature also supports on-the-fly implementation. The proposed method is compatible with any compression algorithm that leverages spatial correlations within the data. The effectiveness of this approach is demonstrated on a large-scale real dataset using several compression methods, including MGARD, SZ, and ZFP., Comment: 6 pages, 9 figures

MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.

Federated Learning (FL) has emerged as a leading paradigm for decentralized, privacy preserving machine learning training. However, recent research on gradient inversion attacks (GIAs) have shown that gradient updates in FL can leak information on private training samples. While existing surveys on GIAs have focused on the honest-but-curious server threat model, there is a dearth of research categorizing attacks under the realistic and far more privacy-infringing cases of malicious servers and clients. In this paper, we present a survey and novel taxonomy of GIAs that emphasize FL threat models, particularly that of malicious servers and clients. We first formally define GIAs and contrast conventional attacks with the malicious attacker. We then summarize existing honest-but-curious attack strategies, corresponding defenses, and evaluation metrics. Critically, we dive into attacks with malicious servers and clients to highlight how they break existing FL defenses, focusing specifically on reconstruction methods, target model architectures, target data, and evaluation metrics. Lastly, we discuss open problems and future research directions.

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) operates in the event mode. Time-of-flight (TOF) information about each detected neutron is collected separately and saved as a descriptive entry in a database enabling unprecedented accuracy of the collected experimental data. Nevertheless, the common data processing pipeline still involves the binning of data to perform analysis and feature extraction. For weak reflections, improper binning leads to sparse histograms with low signal-to-noise ratios, rendering them uninformative. In this study, we propose the Bayesian approach for the identification of Bragg peaks in TOF diffraction data. The method is capable of adaptively handling the varying sampling rates found in different regions of the reciprocal space. Unlike histogram fitting methods, our approach focuses on estimating the true neutron flux function. We accomplish this by employing a profile fitting algorithm based on the event-level likelihood, along with a multiresolution histogram-level prior. By using this approach, we ensure that there is no loss of information due to data reduction in strong reflections and that the search space is appropriately restricted for weak reflections. To demonstrate the effectiveness of our proposed model, we apply it to real experimental data collected at the TOPAZ single crystal diffractometer at SNS.

We describe MGARD, a software providing MultiGrid Adaptive Reduction for floating-point scientific data on structured and unstructured grids. With exceptional data compression capability and precise error control, MGARD addresses a wide range of requirements, including storage reduction, high-performance I/O, and in-situ data analysis. It features a unified application programming interface (API) that seamlessly operates across diverse computing architectures. MGARD has been optimized with highly-tuned GPU kernels and efficient memory and device management mechanisms, ensuring scalable and rapid operations., Comment: 20 pages, 8 figures

Scientific discoveries are increasingly constrained by limited storage space and I/O capacities. For time-series simulations and experiments, their data often need to be decimated over timesteps to accommodate storage and I/O limitations. In this paper, we propose a technique that addresses storage costs while improving post-analysis accuracy through spatiotemporal adaptive, error-controlled lossy compression. We investigate the trade-off between data precision and temporal output rates, revealing that reducing data precision and increasing timestep frequency lead to more accurate analysis outcomes. Additionally, we integrate spatiotemporal feature detection with data compression and demonstrate that performing adaptive error-bounded compression in higher dimensional space enables greater compression ratios, leveraging the error propagation theory of a transformation-based compressor. To evaluate our approach, we conduct experiments using the well-known E3SM climate simulation code and apply our method to compress variables used for cyclone tracking. Our results show a significant reduction in storage size while enhancing the quality of cyclone tracking analysis, both quantitatively and qualitatively, in comparison to the prevalent timestep decimation approach. Compared to three state-of-the-art lossy compressors lacking feature preservation capabilities, our adaptive compression framework improves perfectly matched cases in TC tracking by 26.4-51.3% at medium compression ratios and by 77.3-571.1% at large compression ratios, with a merely 5-11% computational overhead., Comment: 10 pages, 13 figures, 2023 IEEE International Conference on e-Science and Grid Computing

We propose an unsupervised technique for implicit parameterization of data manifolds. In our approach, the data is assumed to belong to a lower dimensional manifold in a higher dimensional space, and the data points are viewed as the endpoints of the trajectories originating outside the manifold. Under this assumption, the data manifold is an attractive manifold of a dynamical system to be estimated. We parameterize such a dynamical system with a residual neural network and propose a spectral localization technique to ensure it is locally attractive in the vicinity of data. We also present initialization and additional regularization of the proposed residual layers. % that we call dissipative bottlenecks. We mention the importance of the considered problem for the tasks of reinforcement learning and support our discussion with examples demonstrating the performance of the proposed layers in denoising and generative tasks.

Anderson acceleration (AA) is an extrapolation technique designed to speed-up fixed-point iterations like those arising from the iterative training of DL models. Training DL models requires large datasets processed in randomly sampled batches that tend to introduce in the fixed-point iteration stochastic oscillations of amplitude roughly inversely proportional to the size of the batch. These oscillations reduce and occasionally eliminate the positive effect of AA. To restore AA's advantage, we combine it with an adaptive moving average procedure that smoothes the oscillations and results in a more regular sequence of gradient descent updates. By monitoring the relative standard deviation between consecutive iterations, we also introduce a criterion to automatically assess whether the moving average is needed. We applied the method to the following DL instantiations: (i) multi-layer perceptrons (MLPs) trained on the open-source graduate admissions dataset for regression, (ii) physics informed neural networks (PINNs) trained on source data to solve 2d and 100d Burgers' partial differential equations (PDEs), and (iii) ResNet50 trained on the open-source ImageNet1k dataset for image classification. Numerical results obtained using up to 1,536 NVIDIA V100 GPUs on the OLCF supercomputer Summit showed the stabilizing effect of the moving average on AA for all the problems above.

We present a nonlocal variational image completion technique which admits simultaneous inpainting of multiple structures and textures in a unified framework. The recovery of geometric structures is achieved by using general convolution operators as a measure of behavior within an image. These are combined with a nonlocal exemplar-based approach to exploit the self-similarity of an image in the selected feature domains and to ensure the inpainting of textures. We also introduce an anisotropic patch distance metric to allow for better control of the feature selection within an image and present a nonlocal energy functional based on this metric. Finally, we derive an optimization algorithm for the proposed variational model and examine its validity experimentally with various test images.

In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as the fixed points of the appropriately chosen nonlinear transformations. We show that this choice leads to the improved stability of both forward and backward propagations, has a favorable impact on the generalization power and allows to control the robustness of the network with only a few hyperparameters. In addition, the proposed reformulation of ResNet does not introduce new parameters and can potentially lead to a reduction in the number of required layers due to improved forward stability. Finally, we derive the memory-efficient training algorithm, propose a stochastic regularization technique and provide numerical results in support of our findings.

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. In this paper, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green's kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal $\epsilon^{-2}$ asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided and the obtained results confirm the efficiency of the considered splitting approach.