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At least 163 records · Page 9

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Physics-informed neural networks (PINNs) have shown to be effective tools for solving both forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network using automatic differentiation, and this PDE loss is evaluated at a set of scattered spatio-temporal points (called residual points). The location and distribution of these residual points are highly important to the performance of PINNs. However, in the existing studies on PINNs, only a few simple residual point sampling methods have mainly been used. Here, we present a comprehensive study of two categories of sampling for PINNs: non-adaptive uniform sampling and adaptive nonuniform sampling. We consider six uniform sampling methods, including (1) equispaced uniform grid, (2) uniformly random sampling, (3) Latin hypercube sampling, (4) Halton sequence, (5) Hammersley sequence, and (6) Sobol sequence. We also consider a resampling strategy for uniform sampling. To improve the sampling efficiency and the accuracy of PINNs, we propose two new residual-based adaptive sampling methods: residual-based adaptive distribution (RAD) and residual-based adaptive refinement with distribution (RAR-D), which dynamically improve the distribution of residual points based on the PDE residuals during training. Hence, we have considered a total of 10 different sampling methods, including six non-adaptive uniform sampling, uniform sampling with resampling, two proposed adaptive sampling, and an existing adaptive sampling. We extensively tested the performance of these sampling methods for four forward problems and two inverse problems in many setups. Our numerical results presented in this study are summarized from more than 6000 simulations of PINNs. Here, we show that the proposed adaptive sampling methods of RAD and RAR-D significantly improve the accuracy of PINNs with fewer residual points for both forward and inverse problems. Furthermore, the results obtained in this study can also be used as a practical guideline in choosing sampling methods.

97 MATHEMATICS AND COMPUTING↗

Industrial control system device classification using network traffic features and neural network embeddings

Characterization of modern cyber–physical Industrial Control System (ICS) devices is critical to the evaluation of their security posture and an understanding of the underlying industrial processes with which they interact. In this work, we address two related ICS device identification tasks: (1) separating ICS from non-ICS devices and (2) identifying specific ICS device types. We propose two distinct methods (one based on the existing IP2Vec method, and a novel traffic-features-based method) for achieving the first task. For transferability of the first task between two datasets, the traffic-features-based method performs significantly better (75% overall accuracy) compared to IP2Vec (22.5% overall accuracy). We further propose a novel method called DNP2Vec to address the second task. DNP2Vec is evaluated on two different datasets and achieves perfect multi-class classification accuracy (100%) for both datasets.

42 ENGINEERING↗

Modular, Hierarchical Learning By Artificial Neural Networks

Modular and hierarchical approach to supervised learning by artificial neural networks leads to neural networks more structured than neural networks in which all neurons fully interconnected. These networks utilize general feedforward flow of information and sparse recurrent connections to achieve dynamical effects. The modular organization, sparsity of modular units and connections, and fact that learning is much more circumscribed are all attractive features for designing neural-network hardware. Learning streamlined by imitating some aspects of biological neural networks.

Baldi, Pierre F.↗

Physically Interpretable Neural Networks for the Geosciences: Applications to Earth System Variability

Abstract Neural networks have become increasingly prevalent within the geosciences, although a common limitation of their usage has been a lack of methods to interpret what the networks learn and how they make decisions. As such, neural networks have often been used within the geosciences to most accurately identify a desired output given a set of inputs, with the interpretation of what the network learns used as a secondary metric to ensure the network is making the right decision for the right reason. Neural network interpretation techniques have become more advanced in recent years, however, and we therefore propose that the ultimate objective of using a neural network can also be the interpretation of what the network has learned rather than the output itself. We show that the interpretation of neural networks can enable the discovery of scientifically meaningful connections within geoscientific data. In particular, we use two methods for neural network interpretation called backward optimization and layerwise relevance propagation, both of which project the decision pathways of a network back onto the original input dimensions. To the best of our knowledge, LRP has not yet been applied to geoscientific research, and we believe it has great potential in this area. We show how these interpretation techniques can be used to reliably infer scientifically meaningful information from neural networks by applying them to common climate patterns. These results suggest that combining interpretable neural networks with novel scientific hypotheses will open the door to many new avenues in neural network‐related geoscience research.

58 GEOSCIENCES↗

On the use of neural networks for energy reconstruction in high-granularity calorimeters

We contrasted the performance of deep neural networks — Convolutional Neural Network (CNN) and Graph Neural Network (GNN) — to current state of the art energy regression methods in a finely 3D-segmented calorimeter simulated by GEANT4. This comparative benchmark gives us some insight to assess the particular latent signals neural network methods exploit to achieve superior resolution. A CNN trained solely on a pure sample of pions achieved substantial improvement in the energy resolution for both single pions and jets over the conventional approaches. It maintained good performance for electron and photon reconstruction. We also used the Graph Neural Network (GNN) with edge convolution to assess the importance of timing information in the shower development for improved energy reconstruction. We implement a simple simulation based correction to the energy sum derived from the fraction of energy deposited in the electromagnetic shower component. This serves as an approximate dual-readout analogue for our benchmark comparison. Although this study does not include the simulation of detector effects, such as electronic noise, the margin of improvement seems robust enough to suggest these benefits will endure in real-world application. We also find reason to infer that the CNN/GNN methods leverage latent features that concur with our current understanding of the physics of calorimeter measurement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Feature-Guided Analysis of Neural Networks

Applying standard software engineering practices to neural networks is challenging due to the lack of high-level abstractions describing a neural network’s behavior. To address this challenge, we propose to extract high-level task-specific features from the neural network internal representation, based on monitoring the neural network activations.The extracted feature representations can serve as a link to high-level requirements and can be leveraged to enable fundamental software engineering activities, such as automated testing, debugging, requirements analysis, and formal verification, leading to better engineering of neural networks. Using two case studies, we present initial empirical evidence demonstrating the feasibility of our ideas.

Features↗

Reinforcement Learning via Gaussian Processes with Neural Network Dual Kernels

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex non-linear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural networks in the kernel domain. We demonstrate that these kernels can be efficiently applied to regression and reinforcement learning problems by analyzing a baseline case study.We apply GPs with neural network dual kernels to solve reinforcement learning tasks for the first time. We demonstrate, using the well understood mountain-car problem, that GPs empowered with dual kernels perform at least as well as those using the conventional radial basis function kernel. Finally, we conjecture that by inheriting the probabilistic rigor of GPs and the powerful embedding properties of DNNs, GPs using NN dual kernels will empower future reinforcement learning models on difficult domains.

97 MATHEMATICS AND COMPUTING↗

Cascade Back-Propagation Learning in Neural Networks

The cascade back-propagation (CBP) algorithm is the basis of a conceptual design for accelerating learning in artificial neural networks. The neural networks would be implemented as analog very-large-scale integrated (VLSI) circuits, and circuits to implement the CBP algorithm would be fabricated on the same VLSI circuit chips with the neural networks. Heretofore, artificial neural networks have learned slowly because it has been necessary to train them via software, for lack of a good on-chip learning technique. The CBP algorithm is an on-chip technique that provides for continuous learning in real time. Artificial neural networks are trained by example: A network is presented with training inputs for which the correct outputs are known, and the algorithm strives to adjust the weights of synaptic connections in the network to make the actual outputs approach the correct outputs. The input data are generally divided into three parts. Two of the parts, called the "training" and "cross-validation" sets, respectively, must be such that the corresponding input/output pairs are known. During training, the cross-validation set enables verification of the status of the input-to-output transformation learned by the network to avoid over-learning. The third part of the data, termed the "test" set, consists of the inputs that are required to be transformed into outputs; this set may or may not include the training set and/or the cross-validation set. Proposed neural-network circuitry for on-chip learning would be divided into two distinct networks; one for training and one for validation. Both networks would share the same synaptic weights.

Duong, Tuan A.↗

Galaxy deblending using residual dense neural networks

We present a new neural network approach for deblending galaxy images in astronomical data using Residual Dense Neural network (RDN) architecture. We train the network on synthetic galaxy images similar to the typical arrangements of field galaxies with a finite point spread function (PSF) and realistic noise levels. The main novelty of our approach is the usage of two distinct neural networks: i) a deblending network which isolates a single galaxy postage stamp from the composite and, ii) a classifier network which counts the remaining number of galaxies. The deblending proceeds by iteratively peeling one galaxy at a time from the composite until the image contains no further objects as determined by the classifier, or by other stopping criteria. By looking at the consistency in the outputs of the two networks, we can assess the quality of the deblending. Further, we characterize the flux and shape reconstructions in different quality bins and compare our deblender with the industry standard, SExtractor. We also discuss possible future extensions for the project with variable PSFs and noise levels.

79 ASTRONOMY AND ASTROPHYSICS↗

Enhancing Lattice Kinetic Schemes for Fluid Dynamics with Lattice-Equivariant Neural Networks

A new class of equivariant neural networks is presented, hereby dubbed lattice-equivariant neural networks (LENNs), designed to satisfy local symmetries of a lattice structure. The approach develops within a recently introduced framework aimed at learning neural network-based surrogate models’ lattice Boltzmann collision operators. Whenever neural networks are employed to model physical systems, respecting symmetries and equivariance properties has been shown to be key for accuracy, numerical stability, and performance. Here, hinging on ideas from group representation theory, trainable layers are defined whose algebraic structure is equivariant with respect to the symmetries of the lattice cell. In this work, the presented method naturally allows for efficient implementations, in terms of both memory usage and computational costs, supporting scalable training/testing for lattices in two spatial dimensions and higher (in which the size of symmetry group grows). The approach is validated and tested considering 2D and 3D flowing dynamics, both in laminar and turbulent regimes. It is compared with group-averaged-based symmetric networks and with plain, nonsymmetric, networks, showing how the presented approach unlocks the (a posteriori) accuracy and training stability of the former models and the train/inference speed of the latter networks. (LENNs are about one order of magnitude faster than group-averaged networks in 3D.) The work in this paper opens toward practical use of machine learning-augmented lattice Boltzmann CFD in real-world simulations.

97 MATHEMATICS AND COMPUTING↗

SNNVis: Visualizing Graph Embedding of Evolutionary Optimization for Spiking Neural Networks

While Spiking Neural Networks (SNNs) show a lot of promise, it is difficult to optimize them because applying traditional gradient-based optimization techniques is difficult. Even though evolutionary algorithms (EAs) have been shown to promise to optimize SNNs, understanding the relationship between evolving the characteristics of SNNs and their performance to improve the optimization algorithm is challenging because of the complex characteristics and huge population size. We propose visual analytics with novel graph embedding for evolutionary SNNs to address the challenges. While existing graph embedding techniques have limitations in preserving the specific features of the nodes and edges, our approach maintains them. Also, we develop visual analytics for understanding the relationship between the network performance and the features of nodes and edges and exploring and analyzing the evolving SNNs to build insights into improving the EA.

Chae, Junghoon [ORNL] (ORCID:0000000206016746)↗

HGQ: High Granularity Quantization for Real-time Neural Networks on FPGAs

Neural networks with sub-microsecond inference latency are required by many critical applications. Targeting such applications deployed on FPGAs, we present High Granularity Quantization (HGQ), a quantization-aware training framework that optimizes parameter bit-widths through gradient descent. Unlike conventional methods, HGQ determines the optimal bit-width for each parameter independently, making it suitable for hardware platforms supporting heterogeneous arbitrary precision arithmetic. In our experiments, HGQ shows superior performance compared to existing network compression methods, achieving orders of magnitude reduction in resource consumption and latency while maintaining the accuracy on several benchmark tasks. These improvements enable the deployment of complex models previously infeasible due to resource or latency constraints. HGQ is open-source and is used for developing next-generation trigger systems at the CERN ATLAS and CMS experiments for particle physics, enabling the use of advanced machine learning models for real-time data selection with sub-microsecond latency.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Orthogonal patterns in binary neural networks

A binary neural network that stores only mutually orthogonal patterns is shown to converge, when probed by any pattern, to a pattern in the memory space, i.e., the space spanned by the stored patterns. The latter are shown to be the only members of the memory space under a certain coding condition, which allows maximum storage of M=(2N) sup 0.5 patterns, where N is the number of neurons. The stored patterns are shown to have basins of attraction of radius N/(2M), within which errors are corrected with probability 1 in a single update cycle. When the probe falls outside these regions, the error correction capability can still be increased to 1 by repeatedly running the network with the same probe.

Baram, Yoram↗

The performance evaluation of a new neural network based traffic management scheme for a satellite communication network

A neural-network-based traffic management scheme for a satellite communication network is described. The scheme consists of two levels of management. The front end of the scheme is a derivation of Kohonen's self-organization model to configure maps for the satellite communication network dynamically. The model consists of three stages. The first stage is the pattern recognition task, in which an exemplar map that best meets the current network requirements is selected. The second stage is the analysis of the discrepancy between the chosen exemplar map and the state of the network, and the adaptive modification of the chosen exemplar map to conform closely to the network requirement (input data pattern) by means of Kohonen's self-organization. On the basis of certain performance criteria, whether a new map is generated to replace the original chosen map is decided in the third stage. A state-dependent routing algorithm, which arranges the incoming call to some proper path, is used to make the network more efficient and to lower the call block rate. Simulation results demonstrate that the scheme, which combines self-organization and the state-dependent routing mechanism, provides better performance in terms of call block rate than schemes that only have either the self-organization mechanism or the routing mechanism.

Ansari, Nirwan↗

Material Data Representation of Hysteresis Loops for Hastelloy X Using Artificial Neural Networks

The artificial neural network (ANN) model proposed by Rumelhart, Hinton, and Williams is applied to develop a functional approximation of material data in the form of hysteresis loops from a nickel-base superalloy, Hastelloy X. Several different ANN configurations are used to model hysteresis loops at different cycles for this alloy. The ANN models were successful in reproducing the hysteresis loops used for its training. However, because of sharp bends at the two ends of hysteresis loops, a drift occurs at the corners of the loops where loading changes to unloading and vice versa (the sharp bends occurred when the stress-strain curves were reproduced by adding stress increments to the preceding values of the stresses). Therefore, it is possible only to reproduce half of the loading path. The generalization capability of the network was tested by using additional data for two other hysteresis loops at different cycles. The results were in good agreement. Also, the use of ANN led to a data compression ratio of approximately 22:1.

Alam, Javed↗