Understanding and Verifying Deep Neural Networks
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Deep Neural Networks↗
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Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network.
Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs [6, 7]. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN’s optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques [8]. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.
97 MATHEMATICS AND COMPUTING↗
Sparse Deep Neural Network Inference using different Programming Models
Sparse deep neural networks have gained increasing attention recently in achieving speedups on inference with reduced memory footprints. However, the real-world applications are little shown with specialized optimizations, yet a wide variety of DNN tasks remain dense without exploiting the advantages of sparsity in networks. Recent work presented by MIT/IEEE/Amazon GraphChallenge has demonstrated significant speedups and various techniques. Still, we find that there is limited investigation of the impact of various Python and C\slash C++ based programming models to explore new opportunities in general cases. In this work, we provide performance evaluation through different programming models using CuPy, cuSPARSE, and OpenMP to discuss the advantages and disadvantages of our sparse implementations on single-GPU and multiple GPUs of NVIDIA DGX-A100 40GB/80GB platforms.
machine learning, HPC↗
Learning model combining convolutional deep neural network with a self-attention mechanism for AC optimal power flow
Alternating current optimal power flow (OPF) analysis is critical for efficient and reliable operation of power systems. For large systems or repetitive computations, the traditional methods such as the direct and gradient methods, or non-traditional methods, such as the genetic algorithm and simulating annealing, are time-consuming and unsuitable for real-time computing. The work in this paper proposes a novel framework to obtain the optimal solution of power flow in real-time using a combination of convolutional neural networks and a self-attention mechanism. All parameters of the power networks are rearranged in an image-like shape of a multi-channel image where each channel is a two-dimensional matrix. The proposed approach is adaptive with every input size of power systems as well as frequent variations of network topologies without intervention to the framework core. The encompassment of all power system contexts in which all parameters of internal elements, generation costs, and topology information are included, contributes to the higher accuracy of inference compared to other current machine-learning-based OPF-solving methods. Besides, the proposed framework established on ubiquitous platforms is effortlessly integrated into current infrastructures of power systems, and the great efficiency along with the computation speed may serve as a critical point for practical implications, such as enabling faster decision-making during real-time operations, predicting system contingencies, and remedial actions based on an offline pre-trained model. Furthermore, this supervised learning process is applied to the dataset of four case studies of meshed power systems: the IEEE 5-bus system (IEEE-5), the IEEE 30-bus system (IEEE-30), the IEEE 39-bus system (IEEE-39), and the IEEE 57-bus system (IEEE-57) to prove the efficacy of the proposed method.
42 ENGINEERING↗
Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification
Full-waveform inversion (FWI) is an accurate imaging approach for modeling the velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We have adopted a neural-network-based full-waveform inversion (NNFWI) method that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, which suppresses noise in the gradients and mitigates local minima. Furthermore, the velocity model generated by neural networks is input to the same partial differential equation (PDE) solvers used in conventional FWI. The gradients of the neural networks and PDEs are calculated using automatic differentiation, which back propagates gradients through the acoustic PDEs and neural network layers to update the weights of the generative neural network. Experiments on 1D velocity models, the Marmousi model, and the 2004 BP model determine that NNFWI can mitigate local minima, especially for imaging high-contrast features such as salt bodies, and it significantly improves the inversion in the presence of noise. Adding dropout layers to the neural network model also allows analyzing the uncertainty of the inversion results through Monte Carlo dropout. NNFWI opens a new pathway to combine deep learning and FWI for exploiting the characteristics of deep neural networks and the high accuracy of PDE solvers. Because NNFWI does not require extra training data and optimization loops, it provides an attractive and straightforward alternative to conventional FWI.
58 GEOSCIENCES↗
Evaluating the Trustworthiness of Deep Neural Networks in Deployment – A Comparative Study (Replicability Study)
As deep neural networks (DNNs) are increasingly used in safety critical applications, there is a growing concern for their trustworthiness. Even highly trained, high-performant networks are not 100% accurate. However, it is very difficult to predict their behaviour during deployment without ground truth. In this paper, we provide a comparative and replicability study on recent approaches that have been proposed to evaluate the trustworthiness of DNNs. We find that it is very difficult to run and reproduce the results for these approaches on their replication packages, and it is even more difficult to run the tools on artifacts other than their own. Further, it is difficult to compare the effectiveness of the tools, due to lack of clearly defined evaluation metrics. Our results indicate that more effort is needed in our research community to obtain sound techniques for evaluating the trustworthiness of neural networks in safety-critical domains. To this end, we contribute an evaluation framework that incorporates the considered approaches and enables evaluation on common benchmarks, using common metrics. Using this framework, we run a comparative study of the three approaches.
Trustworthy AI↗
Physics-constrained deep neural network method for estimating parameters in a redox flow battery
Here, in this paper, we present a physics-constrained deep neural network (PCDNN) method for parameter estimation in the zero-dimensional (0D) model of the vanadium redox flow battery (VRFB). In this approach, we use deep neural networks to approximate the model parameters as functions of the operating conditions. This method allows the integration of VRFB computational models as the physical constraints in the parameter learning process, leading to enhanced accuracy of parameter estimation and cell voltage prediction. Using an experimental dataset, we demonstrate that the PCDNN method can estimate model parameters for a range of operating conditions and improve the 0D model prediction of voltage compared to the 0D model prediction with constant operation-condition-independent parameters estimated with traditional inverse methods. We also demonstrate that the PCDNN approach has an improved generalization ability for estimating parameter values for operating conditions not used in the training process.
25 ENERGY STORAGE↗
Digital Signal Processing Using Deep Neural Networks
Currently there is great interest in the utility of deep neural networks (DNNs) for the physical layer of radio frequency (RF) communications. In this manuscript we describe a custom DNN specially designed to solve problems in the RF domain. Our model leverages the mechanisms of feature extraction and attention through the combination of an autoencoder convolutional network with a transformer network, to accomplish several important communications network and digital signals processing (DSP) tasks. We also present a new open dataset and physical data augmentation model that enables training of DNNs that can perform automatic modulation classification, infer, and correct transmission channel effects, and directly demodulate baseband RF signals.
42 ENGINEERING↗
An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture
This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.
42 ENGINEERING↗
Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling
Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.
Bayesian optimization↗
TorchBraid: High-Performance Layer-Parallel Training of Deep Neural Networks with MPI and GPU Acceleration
TorchBraid is a high-performance implementation of layer-parallel training for deep neural networks (DNNs) supporting MPI-based parallelism and GPU acceleration. Layer-parallel training has been developed to overcome the serialization inherent in forward and backward propagation of DNNs that limits utilization of computational resources in the strong scaling limit. To achieve this, TorchBraid integrates the PyTorch neural network framework with the state-of-the-art XBraid time-parallel library. Furthermore, this article presents the use and performance of TorchBraid, in addition to solutions for overcoming the algorithmic challenges inherent in combining automatic differentiation with layer-parallel. Results are presented with and without GPU acceleration for the Tiny ImageNet and MNIST image classification data sets, as well as recurrent neural networks. Overall, TorchBraid enables fast training of DNNs, both in a strong and weak scaling context. In addition to the TorchBraid software, several new advances in applying layer-parallel algorithms are detailed. Integration of layer-parallel with data-parallel algorithms is presented for the first time, showing the computational advantages of the combination. Standard deep learning techniques, like batch-normalization, are developed for layer-parallel training. Finally, a new approach combining layer-parallel with spatial coarsening in order to accelerate training for 3D image classification shows roughly a 10× speedup over serial execution.
Layer-parallel↗
Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representations
We introduce and investigate, for finite groups G, G-invariant deep neural network (GDNN) architectures with ReLU activation that are densely connected- i.e., include all possible skip connections. In contrast to other G-invariant architectures in the literature, the preactivations of theG-DNNs presented here are able to transform by signed permutation representations (signed perm-reps) of G. Moreover, the individual layers of the G-DNNs are not required to be G-equivariant; instead, the preactivations are constrained to be G-equivariant functions of the network input in a way that couples weights across all layers. The result is a richer family of G-invariant architectures never seen previously. We derive an efficient implementation of G-DNNs after a reparameterization of weights, as well as necessary and sufficient conditions for an architecture to be "admissible"- i.e., nondegenerate and inequivalent to smaller architectures. We include code that allows a user to build a G-DNN interactively layer-by-layer, with the final architecture guaranteed to be admissible. We show that there are far more admissible G-DNN architectures than those accessible with the "concatenated ReLU" activation function from the literature. Finally, we apply G-DNNs to two example problems--(1) multiplication in --1, 1} (with theoretical guarantees) and (2) 3D object classification--finding that the inclusion of signed perm-reps significantly boosts predictive performance compared to baselines with only ordinary (i.e., unsigned) perm-reps.
97 MATHEMATICS AND COMPUTING↗
Improving Deep Neural Networks’ Training for Image Classification With Nonlinear Conjugate Gradient-Style Adaptive Momentum
Momentum is crucial in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated constant. However, tuning the hyperparameter for momentum can be a significant computational burden. In this article, we propose a novel adaptive momentum for improving DNNs training; this adaptive momentum, with no momentum-related hyperparame- ter required, is motivated by the nonlinear conjugate gradient (NCG) method. Stochastic gradient descent (SGD) with this new adaptive momentum eliminates the need for the momentum hyperparameter calibration, allows using a significantly larger learning rate, accelerates DNN training, and improves the final accuracy and robustness of the trained DNNs. For example, SGD with this adaptive momentum reduces classification errors for training ResNet110 for CIFAR10 and CIFAR100 from 5.25% to 4.64% and 23.75% to 20.03%, respectively. Furthermore, SGD, with the new adaptive momentum, also benefits adversarial training and, hence, improves the adversarial robustness of the trained DNNs.
97 MATHEMATICS AND COMPUTING↗
Deep Neural Network Based Convergence Classification for Computational Fluid Dynamics
A supervised deep learning approach is coupled with heuristic convergence criteria to construct a classification model for detecting the completion (convergence) of computational fluid dynamics (CFD) simulations. Heuristic convergence criteria alone are not always sufficient and more complex decisions are often left to a human analyst. The proposed approach leverages heuristic convergence criteria as well as two deep neural network (DNN) models, one binary and one multi-class, to improve the efficiency and consistency of convergence classification across a wide range of flight regimes. The DNN models presented are each trained on a subset of ascent aerodynamic CFD simulations for NASA’s Space Launch System and were produced using NASA’s unstructured Navier-Stokes solver FUN3D. Individual solutions are analyzed intermittently and are classified as sufficiently converged, further iterations required, or switch from steady Reynolds Averaged Navier-Stokes (RANS) to unsteady RANS CFD based on the iterative histories of four aerodynamic coefficients. The implemented classification model is shown to produce solutions that closely correlate to solutions produced by a human analyst. This work lays groundwork for expanding the capabilities of DNNs for automating and improving more of the CFD process.
SLS↗
Deep Neural Network Based Unsteady Flamelet Progress Variable Approach in a Supersonic Combustor
Higher dimensional flamelet manifolds are essential in capturing the coupled effects of pressure gradients and unsteady chemical kinetics observed in supersonic combustion applications. Previous studies have validated the feasibility of using deep neural networks as an alternative to computation-ally intensive multidimensional flamelet table storage and lookup. This approach has demonstrated a significant reduction in memory footprint and enabled the use of larger dimensional tabulated manifolds for supersonic combustion in canonical problems. In this study, the Unsteady Flamelet Progress Variable (UFPV)-ANN model implemented in the VULCAN-CFD code is validated by the Burrows-Kurkov supersonic mixing/combustion configuration. The well characterized experimental problem consists of hydrogen injection into a supersonic vitiated crossflow that results in a lifted flame structure. The initial model consists of a 4-dimensional table where the independent variables Z, C, Xst, P are tabulated using an unsteady flamelet code with boundary conditions corresponding to the vitiated air conditions. The results show the development of a lifted flame structure and over-all acceptable agreement with finite-rate chemistry (FRC) simulation and the experimental data. Moreover, direct mapping between the independent variables and the flamelet table is replaced by a deep neural network for significant memory reduction. The results indicate that the UFPV-ANN approach can retrieve the same solution as the memory intensive lookup table approach.
Flamelet↗
Modeling Liquid Water by Climbing up Jacob’s Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials
Within the framework of Kohn–Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric–isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Understanding the surface wave characteristics using 2D particle-in-cell simulation and deep neural network
Here, the characteristics of the surface waves along the interface between a plasma and a dielectric material have been investigated using kinetic particle-in-cell simulations. A microwave source of GHz frequency has been used to trigger the surface wave in the system. The outcome indicates that the surface wave gets excited along the interface of plasma and the dielectric tube and appears as light and dark patterns in the electric field profiles. The dependency of radiation pressure on the dielectric permittivity and supplied input frequency has been investigated. Further, we assessed the capabilities of neural networks to predict the radiation pressure for a given system. The proposed deep neural network model is aimed at developing accurate and efficient data-driven plasma surface wave devices.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
MDLoader: A Hybrid Model-driven Data Loader for Distributed Deep Neural Networks Training
In this work, we propose MD Loader, a hybrid in-memory data loader for distributed deep neural networks. MDLoader introduces a model-driven performance estimator to automatically switch between one-sided and collective communication at runtime.
Bae, Jonghyun↗