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At least 1,099 records · Page 61

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .

97 MATHEMATICS AND COMPUTING↗

Convolutional Neural Networks for Problems in Transport Phenomena: A Theoretical Minimum

Convolutional neural network (CNN), a deep learning algorithm, has gained popularity in technological applications that rely on interpreting images (typically, an image is a 2D field of pixels). Transport phenomena is the science of studying different fields representing mass, momentum, or heat transfer. Some of the common fields are species concentration, fluid velocity, pressure, and temperature. Each of these fields can be expressed as an image(s). Consequently, CNNs can be leveraged to solve specific scientific problems in transport phenomena. Herein, we show that such problems can be grouped into three basic categories: (a) mapping a field to a descriptor (b) mapping a field to another field, and (c) mapping a descriptor to a field. After reviewing the representative transport phenomena literature for each of these categories, we illustrate the necessary steps for constructing appropriate CNN solutions using sessile liquid drops as an exemplar problem. If sufficient training data is available, CNNs can considerably speed up the solution of the corresponding problems. Finally, the present discussion is meant to be minimalistic such that readers can easily identify the transport phenomena problems where CNNs can be useful as well as construct and/or assess such solutions.

97 MATHEMATICS AND COMPUTING↗

Transfer learning for metamaterial design and simulation

Abstract We demonstrate transfer learning as a tool to improve the efficacy of training deep learning models based on residual neural networks (ResNets). Specifically, we examine its use for study of multi-scale electrically large metasurface arrays under open boundary conditions in electromagnetic metamaterials. Our aim is to assess the efficiency of transfer learning across a range of problem domains that vary in their resemblance to the original base problem for which the ResNet model was initially trained. We use a quasi-analytical discrete dipole approximation (DDA) method to simulate electrically large metasurface arrays to obtain ground truth data for training and testing of our deep neural network. Our approach can save significant time for examining novel metasurface designs by harnessing the power of transfer learning, as it effectively mitigates the pervasive data bottleneck issue commonly encountered in deep learning. We demonstrate that for the best case when the transfer task is sufficiently similar to the target task, a new task can be effectively trained using only a few data points yet still achieve a test mean absolute relative error of 3 % with a pre-trained neural network, realizing data reduction by a factor of 1000.

Peng, Rixi↗

Enabling deeper learning on big data for materials informatics applications

Abstract The application of machine learning (ML) techniques in materials science has attracted significant attention in recent years, due to their impressive ability to efficiently extract data-driven linkages from various input materials representations to their output properties. While the application of traditional ML techniques has become quite ubiquitous, there have been limited applications of more advanced deep learning (DL) techniques, primarily because big materials datasets are relatively rare. Given the demonstrated potential and advantages of DL and the increasing availability of big materials datasets, it is attractive to go for deeper neural networks in a bid to boost model performance, but in reality, it leads to performance degradation due to the vanishing gradient problem. In this paper, we address the question of how to enable deeper learning for cases where big materials data is available. Here, we present a general deep learning framework based on Individual Residual learning (IRNet) composed of very deep neural networks that can work with any vector-based materials representation as input to build accurate property prediction models. We find that the proposed IRNet models can not only successfully alleviate the vanishing gradient problem and enable deeper learning, but also lead to significantly (up to 47%) better model accuracy as compared to plain deep neural networks and traditional ML techniques for a given input materials representation in the presence of big data.

36 MATERIALS SCIENCE↗

Low Activity Tritium Detection in CCDs Using Deep Learning Techniques

Here, this study explores the use of charge-coupled devices (CCDs) for detecting low-energy beta particles from tritium decay - a critical signal for nuclear safety, nuclear nonproliferation, and environmental monitoring. We employ a dual approach utilizing both measured CCD data and detailed Geant4 simulations. Our analysis compares classical techniques with advanced deep learning methods, including convolutional neural networks (CNNs), autoencoders trained exclusively on tritium data, and preliminary studies on boosted decision trees (BDTs). The CNN, trained on mixed signal/background datasets, demonstrates superior classification performance, while the autoencoder shows the potential of unsupervised, background-agnostic strategies when background characteristics are poorly defined. These results highlight the excellent sensitivity achievable thanks to the background rejection made possible by information-rich CCD data, paving the way for improved portable tritium monitoring.

Autoencoder↗

DCTRGAN: improving the precision of generative models with reweighting

Significant advances in deep learning have led to more widely used and precise neural network-based generative models such as Generative Adversarial Networks (Gans). We introduce a post-hoc correction to deep generative models to further improve their fidelity, based on the Deep neural networks using the Classification for Tuning and Reweighting (Dctr) protocol. The correction takes the form of a reweighting function that can be applied to generated examples when making predictions from the simulation. We illustrate this approach using Gans trained on standard multimodal probability densities as well as calorimeter simulations from high energy physics. We show that the weighted Gan examples significantly improve the accuracy of the generated samples without a large loss in statistical power. This approach could be applied to any generative model and is a promising refinement method for high energy physics applications and beyond.

47 OTHER INSTRUMENTATION↗

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗

Bridging the Gap between Cosmological Simulations with Graph Neural Networks and Domain Adaptation

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross dataset tasks (up to 28% better relative error and up to almost an order of magnitude better χ 2 ). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

97 MATHEMATICS AND COMPUTING↗

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Lessons learned from the two largest Galaxy morphological classification catalogues built by convolutional neural networks

ABSTRACT We compare the two largest galaxy morphology catalogues, which separate early- and late-type galaxies at intermediate redshift. The two catalogues were built by applying supervised deep learning (convolutional neural networks, CNNs) to the Dark Energy Survey data down to a magnitude limit of ∼21 mag. The methodologies used for the construction of the catalogues include differences such as the cutout sizes, the labels used for training, and the input to the CNN – monochromatic images versus gri-band normalized images. In addition, one catalogue is trained using bright galaxies observed with DES (i < 18), while the other is trained with bright galaxies (r < 17.5) and ‘emulated’ galaxies up to r-band magnitude 22.5. Despite the different approaches, the agreement between the two catalogues is excellent up to i < 19, demonstrating that CNN predictions are reliable for samples at least one magnitude fainter than the training sample limit. It also shows that morphological classifications based on monochromatic images are comparable to those based on gri-band images, at least in the bright regime. At fainter magnitudes, i > 19, the overall agreement is good (∼95 per cent), but is mostly driven by the large spiral fraction in the two catalogues. In contrast, the agreement within the elliptical population is not as good, especially at faint magnitudes. By studying the mismatched cases, we are able to identify lenticular galaxies (at least up to i < 19), which are difficult to distinguish using standard classification approaches. The synergy of both catalogues provides an unique opportunity to select a population of unusual galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Graph neural networks for CO 2 solubility predictions in Deep Eutectic Solvents

Deep Eutectic Solvents (DESs) are a promising class of solvents for CO 2 capture. DESs are complex mixtures that can be designed to optimize CO solubility and overall capture process efficiency. However, the vast design landscape of DES mixtures makes experimental investigation prohibitive; as such, there is a need for computational models that can quickly and efficiently navigate the design space and inform data collection efforts. In this work, we propose Graph Neural Network (GNN) models for predicting CO 2 solubility for DESs; the GNN leverages a mixture graph representation that captures the molecular structure of the DES components as well as their intermolecular interactions. Here, we compare the GNN framework against alternative architectures (neural networks, graph convolution networks, and random forests) and data representations (molecular fingerprints, sigma profiles, and graphs). We show that the proposed approach offers superior predictive performance; specifically, we show that solubility can be predicted reliably directly from molecular structure (without the need of using sigma profiles as proposed in previous studies). This result is important, as obtaining sigma profiles requires expensive density functional theory computations. We also explored the ability of GNNs to predict solubility for new DES mixtures and operating conditions. We found that the model extrapolates across temperature reliably. However, we also found deficiencies in the ability of the model to predict solubility for DES mixtures, pressures, and molar ratio not included in the training sets; we show that this is due to an inherent lack of chemical diversity in datasets available in the literature. The proposed computational capabilities can thus help navigate the design space of DES and inform data collection efforts. Our models, data, and benchmarks are shared as Python code implemented in Jupyter notebooks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

TPSAS-NF1676L-32014-DND

The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), on-board the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) is a satellite-borne polarization sensitive lidar. It has been providing the vertical distributions of clouds and aerosols along with their microphysical and optical properties since 2006. One of its important Level 2 products, feature classification, has been determined using the lidar information from 532 nm parallel and perpendicular channels, and 1064 nm channel measurements of layer integrated backscatter. Deep machine learning methods which combine both the channel and texture information to recognize feature patterns is uniquely beneficial when applied to this data. In this study, we will use Convolutional Neural Network (CNN), a deep machine learning method, to classify lidar aerosol subtypes by using the lidar profile observations. This method uses additional information from the vertical texture of the feature instead of using only the layer information. Note that in the integrated layer properties, the texture information has been masked due to averaging. Our results will show how the texture information plays a role in the classification. This preliminary work explores the benefits and potential of deep machine learning methods for lidar retrievals and focuses on the aerosol subtype classification. The broader application extends to the classification of other feature types. Future applications include the developing deep machine learning methods with neural networks to retrieve properties of the features, and studies of indirect effect of cloud-aerosol interaction from lidar measurements.

Shan Zeng Kowalski↗

Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?

Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning, the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but under-rated area is uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions, due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of UQ of ML. We will elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling will be discussed, demonstrated, and compared. We will also present and demonstrate a few techniques to quantify the ML prediction uncertainties, including Monte Carlo dropout, deep ensemble, Bayesian neural networks, Gaussian Processes and conformal prediction. Lastly, we will discuss the need for building a verification, validation and UQ framework to establish ML credibility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational science and engineering. Guided by data and physical laws, PINNs find a neural network that approximates the solution to a system of PDEs. Such a neural network is obtained by minimizing a loss function in which any prior knowledge of PDEs and data are encoded. Despite its remarkable empirical success in one, two or three dimensional problems, there is little theoretical justification for PINNs. As the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We want to answer the question: Does the sequence of minimizers converge to the solution to the PDE? We consider two classes of PDEs: linear second-order elliptic and parabolic. By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in C 0 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes H 1 . Computational examples are provided to illustrate our theoretical findings. To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs.

97 MATHEMATICS AND COMPUTING↗

Neutrino interaction classification with a convolutional neural network in the DUNE far detector

The Deep Underground Neutrino Experiment is a next-generation neutrino oscillation experiment that aims to measure $CP$-violation in the neutrino sector as part of a wider physics program. A deep learning approach based on a convolutional neural network has been developed to provide highly efficient and pure selections of electron neutrino and muon neutrino charged-current interactions. The electron neutrino (antineutrino) selection efficiency peaks at 90% (94%) and exceeds 85% (90%) for reconstructed neutrino energies between 2-5 GeV. The muon neutrino (antineutrino) event selection is found to have a maximum efficiency of 96% (97%) and exceeds 90% (95%) efficiency for reconstructed neutrino energies above 2 GeV. When considering all electron neutrino and antineutrino interactions as signal, a selection purity of 90% is achieved. These event selections are critical to maximize the sensitivity of the experiment to $CP$-violating effects.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The predictive skill of convolutional neural networks models for disease forecasting

In this paper we investigate the utility of one-dimensional convolutional neural network (CNN) models in epidemiological forecasting. Deep learning models, in particular variants of recurrent neural networks (RNNs) have been studied for ILI (Influenza-Like Illness) forecasting, and have achieved a higher forecasting skill compared to conventional models such as ARIMA. In this study, we adapt two neural networks that employ one-dimensional temporal convolutional layers as a primary building block—temporal convolutional networks and simple neural attentive meta-learners—for epidemiological forecasting. We then test them with influenza data from the US collected over 2010-2019. We find that epidemiological forecasting with CNNs is feasible, and their forecasting skill is comparable to, and at times, superior to, plain RNNs. Thus CNNs and RNNs bring the power of nonlinear transformations to purely data-driven epidemiological models, a capability that heretofore has been limited to more elaborate mechanistic/compartmental disease models.

59 BASIC BIOLOGICAL SCIENCES↗

Simurgh: A Framework for Cad-Driven Deep Learning Based X-Ray CT Reconstruction

High-resolution X-ray computed tomography (XCT) is an important technique for the inspection of additively manufactured (AM) parts. While XCT is typically used off-line to inspect a subset of manufactured parts, significantly accelerating measurement speed while retaining accuracy would enable use of XCT for in-line inspection to rapidly identify defects in each part as it is manufactured. Here, we propose a deep learning (DL) based approach that uses computer aided design (CAD) models of the AM parts and physics-based information to rapidly produce high-quality reconstructions from sparse XCT measurements without high quality ground truth data. Our approach uses a generative adversarial neural network (GAN) to produced realistic training data from the CAD-based simulations and a deep neural network that is trained using data from the first stage to produce accurate 3D reconstructions. Using experimental XCT data of metal parts, we demonstrate enhanced defect detection capabilities while dramatically reducing the scan time.

Ziabari, Amir↗

An Ensemble of Neural Networks for Moist Physics Processes, Its Generalizability and Stable Integration

Abstract With the recent advances in data science, machine learning has been increasingly applied to convection and cloud parameterizations in global climate models (GCMs). This study extends the work of Han et al. (2020, https://doi.org/10.1029/2020MS002076 ) and uses an ensemble of 32‐layer deep convolutional residual neural networks, referred to as ResCu‐en, to emulate convection and cloud processes simulated by a superparameterized GCM, SPCAM. ResCu‐en predicts GCM grid‐scale temperature and moisture tendencies, and cloud liquid and ice water contents from moist physics processes. The surface rainfall is derived from the column‐integrated moisture tendency. The prediction uncertainty inherent in deep learning algorithms in emulating the moist physics is reduced by ensemble averaging. Results in 1‐year independent offline validation show that ResCu‐en has high prediction accuracy for all output variables, both in the current climate and in a warmer climate with +4K sea surface temperature. The analysis of different neural net configurations shows that the success to generalize in a warmer climate is attributed to convective memory and the 1‐dimensional convolution layers incorporated into ResCu‐en. We further implement a member of ResCu‐en into CAM5 with real world geography and run the neural‐network‐enabled CAM5 (NCAM) for 5 years without encountering any numerical integration instability. The simulation generally captures the global distribution of the mean precipitation, with a better simulation of precipitation intensity and diurnal cycle. However, there are large biases in temperature and moisture in high latitudes. These results highlight the importance of convective memory and demonstrate the potential for machine learning to enhance climate modeling.

Meteorology & Atmospheric Sciences↗