Search NASA⌕ Search

SEARCH · Search NASA

Results for “differentiable machine learning”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗
DOE OSTI2018

Neural Algorithms for Low Power Implementation of Partial Differential Equations

The rise of low-power neuromorphic hardware has the potential to change high-performance computing; however much of the focus on brain-inspired hardware has been on machine learning applications. A low-power solution for solving partial differential equations could radically change how we approach large-scale computing in the future. The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking neuromorphic hardware. The first method tracks the positions of individual walkers independently by using a modular code inspired by grid cells in the brain. The second method tracks the densities of random walkers at each spatial location directly. We present the scaling complexity of each of these methods and illustrate their ability to model random walkers under different probabilistic conditions. Finally, we present implementations of these algorithms on neuromorphic hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Example on how to (intelligently) augment the nuclear-data pipeline with machine learning [Slides]

The presentation discusses how machine learning has helped the Los Alamos National Laboratory (LANL) nuclear-data pipeline. It also discusses the strengths of machine learning as it finds trends in large amounts of data where human brains are overwhelmed and that this information may be crucial to improve our nuclear data. It does stress, however, that machine learning is no "silver bullet" and that it is critical to feed it expert knowledge and use physics intuition to interpret the results. The presentation discusses the need to develop infrastructure and tools to provide data in an easily readable and unambiguously interpretable format (e.g., EXFOR format), to develop experimental data and theory to solve physics questions, and that statisticians and nuclear-data experts must be brought together to correctly interpret the results. The presentation concludes by stating that machine learning is a great tool and that LANL needs to use the algorithms along with developing physics data, tools and infrastructure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

MADLens, a python package for fast and differentiable non-Gaussian lensing simulations

Here, we present MADLens a python package for producing non-Gaussian lensing convergence maps at arbitrary source redshifts with unprecedented precision. MADLens is designed to achieve high accuracy while keeping computational costs as low as possible. A MADLens simulation with only particles produces convergence maps whose power agrees with theoretical lensing power spectra up to within the accuracy limits of HaloFit. This is made possible by a combination of a highly parallelizable particle-mesh algorithm, a sub-evolution scheme in the lensing projection, and a machine-learning inspired sharpening step. Further, MADLens is fully differentiable with respect to the initial conditions of the underlying particle-mesh simulations and a number of cosmological parameters. These properties allow MADLens to be used as a forward model in Bayesian inference algorithms that require optimization or derivative-aided sampling. Another use case for MADLens is the production of large, high resolution simulation sets as they are required for training novel deep-learning-based lensing analysis tools. We make the MADLens package publicly available under a Creative Commons License

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Modeling MTS pyrolysis and SiC deposition kinetics using principal component analysis and neural networks

Accurate chemical kinetics modeling is crucial for improving the efficiency of chemical processing and synthesis of ceramic matrix composites. Detailed kinetic models are computationally expensive due to the large number of transported chemical species, while the simplified physics-based models, such as single-step global mechanisms, are efficient but often overlook key chemical intermediates and pathways. Recent deep learning approaches promise accurate and cost-effective models. Yet, they require additional closures for the transported nonlinear latent variables, complicating integration with existing solvers. In this work, we develop a hybrid linear—nonlinear reduced model for silicon carbide deposition from methyltrichlorosilane precursor by combining principal component analysis (PCA) and autoencoder (AE) neural network (NN) approaches. PCA is used to identify a smaller set of linear transport variables, enabling direct reuse of conventional transport solvers. NNs then reconstruct the full chemical state from these reduced variables. We demonstrate the method on a chemical vapor deposition reactor—comprising a gas-phase pyrolysis plug flow reactor and a heterogeneous surface reactor—over a wide range of temperatures, pressures, and residence times. Our PCA–AE model achieves high accuracy with only five transported scalars, achieving an eightfold cost reduction compared to detailed mechanisms, in both a priori (using data from the test set only) and a posteriori (coupled with a differential equation solver). In conclusion, notable errors arise primarily near training domain boundaries and for long residence times, indicating the need for domain shift indicators and better long-horizon predictions in future reduced chemistry model development.

autoencoder neural networks↗
DOE OSTI2020

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

For centuries, flow visualization has been the art of making fluid motion visible in physical and biological systems. Although such flow patterns can be, in principle, described by the Navier-Stokes equations, extracting the velocity and pressure fields directly from the images is challenging. We addressed this problem by developing hidden fluid mechanics (HFM), a physics-informed deep-learning framework capable of encoding the Navier-Stokes equations into the neural networks while being agnostic to the geometry or the initial and boundary conditions. We demonstrate HFM for several physical and biomedical problems by extracting quantitative information for which direct measurements may not be possible.

Raissi, Maziar↗
DOE OSTI2023

Using machine learning to predict the correlation of spectra using SDSS magnitudes as an improvement to the Locus Algorithm

The Locus Algorithm is a new technique to improve the quality of differential photometry by optimising the choices of reference stars. At the heart of this algorithm is a routine to assess how good each potential reference star is by comparing its SDSS magnitude values to those of the target star. In this way, the difference in wavelength-dependent effects of the Earth’s atmospheric scattering between target and reference can be minimised. This paper sets out a new way to estimate the quality of each reference star using machine learning. A random subset of stars from SDSS with spectra was chosen. For each one, a suitable reference star, also with a spectrum, was chosen. The correlation between the two spectra in the SDSS r band (between 550 nm and 700 nm) was taken to be the gold-standard measure of how well they match up for differential photometry. The five SDSS magnitude values for each of these stars were used as predictors. A number of supervised machine learning models were constructed on a training set of the stars and were each evaluated on a testing set. The model using Support Vector Regression had the best performance of these models. It was then tested on a final, hold-out, validation set of stars to get an unbiased measure of its performance. With an R 2 of 0.62, the SVR model presents enhanced performance for the Locus Algorithm technique.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Design of a neutral thermal scattering (NeTS) module for hydrogen in light water

The accurate representation of thermal scattering law (TSL) data is integral to the design and characterization of many modern nuclear systems, particularly those using light water as a moderator/coolant. As a material-dependent distribution over energy-momentum phase space, the TSL may exhibit a variety of unique and relevant conditional (e.g., temperature, pressure) and compositional (e.g., porosity, stoichiometry, radiation damage) dependencies. Currently, there are various approaches to incorporate temperature dependence, which is especially important in coupled neutronic-thermal hydraulic simulations. In each approach, there is an inherent tradeoff between memory consumption and accuracy. Some techniques require tens to hundreds of MBs or more, while others fail to reproduce the underlying data to within 10% error over the considered input domain, despite having a reduced storage burden. This work aims to address both sides of the tradeoff simultaneously by implementing a novel deep learning (DL) approach to TSL representation. The neural thermal scattering (NeTS) concept, which is amenable to an arbitrary number of dependencies, is demonstrated via the inclusion of temperature dependence into a highly compact, highly accurate functional form of the multi- variate TSL (i.e., S(α, β, T)) for hydrogen in light water. Resulting storage requirements are on the order of 100 kB, and median and maximum percent deviations are on the order of 0.1% and 1%, respectively. These measures represent a step improvement over previous techniques. Notably, the developed neural network and feature methodology build on those employed in prior work on beryllium oxide. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

LENS: Learning Enabled Network Synthesis

RTRC and UMD have developed novel machine learning based methods under the ARPA-E DIFFERENTIATE program for rapid acceleration of hypothesis generation in complex architecture design spaces involving both discrete choices of component inclusion and interconnection and continuous parametric decisions. The project named Learning Enabled Network Synthesis (LENS) further demonstrated the developed methods on challenging electrical power converter design problems by identifying the most suitable circuit topologies and simultaneously selecting the most appropriate components to achieve optimized design of power converter with improved performances. We demonstrated that LENS could enable exploration of very large design space of circuit topologies and components by addressing the limitations of conventional design process in non-linear, high switching speed, multi-dimensional power converter design and optimization. The key innovation developed in LENS is the seamless integration of statistical learning and logical reasoning techniques and building on the individual strengths of these techniques for rapid hypothesis discovery. The main component of LENS comprises of: 1) Graph Reasoning Engine (GRE) to enforce composition rules that rapidly reject all discrete architectures that are composed incorrectly and generates an adaptive database of feasible designs which can be used by ML modules, 2) Graph Generative Learning module which is a deep neural network based generative model for graph architectures which can enable design space exploration beyond the dataset generated by the GRE, 3) Graph Reduced Order Model (ROM) for graph domains for accelerating computation of output metrics, and 4) Active learning and Rule Discovery module for sample efficient learning and extracting logical rules from the learned ML models which will be integrated in the GRE to enhance the filtering effectiveness. LENS approach can be applied to any design domains where designs can be represented as multi-attribute graphs. The LENS team integrated the various technical innovations listed above into an optimization pipeline and exercised the optimization pipeline on the converter design problem. The LENS project demonstrated that the developed AI/ML technologies can be used to generate novel converter circuits >45x faster than experts on chosen use-cases. This can enable faster design space exploration and identification of new designs which are not considered by experts due to the increasing design space complexity. This has significant potential impact on the public and energy needs of the country. It is currently estimated that 30% of all electrical powers generated passes through power converters. The future estimate is that 80% of all power generated would be passing through converters. LENS fills a critical gap in this space since by accelerating the design process the designers would be able to generate more efficient converters which can lead to significant energy savings for the country.

42 ENGINEERING↗
DOE OSTI2024

Simultaneous Unbinned Differential Cross-Section Measurement of Twenty-Four Z+jets Kinematic Observables with the ATLAS Detector

Z boson events at the Large Hadron Collider can be selected with high purity and are sensitive to a diverse range of QCD phenomena. As a result, these events are often used to probe the nature of the strong force, improve Monte Carlo event generators, and search for deviations from standard model predictions. All previous measurements of Z boson production characterize the event properties using a small number of observables and present the results as differential cross sections in predetermined bins. In this analysis, a machine learning method called omnifold is used to produce a simultaneous measurement of twenty-four Z +jets observables using 139 fb -1 of proton-proton collisions at √s =13 TeV collected with the ATLAS detector. Unlike any previous fiducial differential cross-section measurement, this result is presented unbinned as a dataset of particle-level events, allowing for flexible reuse in a variety of contexts and for new observables to be constructed from the twenty-four measured observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Learning physics-based reduced-order models from data using nonlinear manifolds

Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

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↗
DOE OSTI2026

Reconstruction of Six-Dimensional Phase Space

A phase space is a mathematical representation of all possible physical states of a system. Particle beams at Fermilab exist within a six-dimensional (6D) phase space defined by three positional components, (x, y, z) and three momentum components, (px, py, pz). To reconstruct this space implies taking measurement data from detectors and mapping out particle behavior using computational methods. The beam detectors, however, are only able to detect spatial distribution among the events of the beam, therefore being limited to positional data. Also, due to the vast number of events in a particle beam, it is extremely difficult to analyze and differentiate every single one’s behavior. However, with Machine Learning (ML), which can distinguish between patterns and map out particle behavior more efficiently. We first used the particle beam software, G4beamline, to simulate a 10,000-event muon beam, adjusting parameters such as initial momentum magnitude (p¬0) and virtual detector position. Using ten virtual detectors, we analyzed p0 values such that minimum 9,990 events were analyzed by every detector. We then input the data from these beam simulations to a C++ program, that randomly selects 100 events, and creates a 2D histogram based on spatial distribution, detector position, and event intensity. This process is repeated 100 times to create 100 histograms per p0 value. These images were then input to a modified ResNet18 Convolutional Neural Network (CNN) for training, and to predict p0 from some unseen set of histograms. The model was accurate when trained on momentum increments of 5 MeV/c and provided with denser training samples around highly variable test values. These results displayed machine learning being able to accurately predict p0 from being trained on different particle behaviors.

Shirlee, Jermain [Fermilab]↗
DOE OSTI2022

New directions for surrogate models and differentiable programming for High Energy Physics detector simulation

The computational cost for high energy physics detector simulation in future experimental facilities is going to exceed the current available resources. To overcome this challenge, new ideas on surrogate models using machine learning methods are being explored to replace computationally expensive components. Additionally, differentiable programming has been proposed as a complementary approach, providing controllable and scalable simulation routines. In this document, new and ongoing efforts for surrogate models and differential programming applied to detector simulation are discussed in the context of the 2021 Particle Physics Community Planning Exercise (`Snowmass').

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Application of convolutional neural networks for stellar spectral classification

ABSTRACT Due to the ever-expanding volume of observed spectroscopic data from surveys such as SDSS and LAMOST, it has become important to apply artificial intelligence (AI) techniques for analysing stellar spectra to solve spectral classification and regression problems like the determination of stellar atmospheric parameters Teff, $\rm {\log g}$, and [Fe/H]. We propose an automated approach for the classification of stellar spectra in the optical region using convolutional neural networks (CNNs). Traditional machine learning (ML) methods with ‘shallow’ architecture (usually up to two hidden layers) have been trained for these purposes in the past. However, deep learning methods with a larger number of hidden layers allow the use of finer details in the spectrum which results in improved accuracy and better generalization. Studying finer spectral signatures also enables us to determine accurate differential stellar parameters and find rare objects. We examine various machine and deep learning algorithms like artificial neural networks, Random Forest, and CNN to classify stellar spectra using the Jacoby Atlas, ELODIE, and MILES spectral libraries as training samples. We test the performance of the trained networks on the Indo-U.S. Library of Coudé Feed Stellar Spectra (CFLIB). We show that using CNNs, we are able to lower the error up to 1.23 spectral subclasses as compared to that of two subclasses achieved in the past studies with ML approach. We further apply the trained model to classify stellar spectra retrieved from the SDSS data base with SNR > 20.

Sharma, Kaushal↗
DOE OSTI2024

RNA Splicing Events in Circulation Distinguish Individuals With and Without New-onset Type 1 Diabetes

Context: Alterations in RNA splicing may influence protein isoform diversity that contributes to or reflects the pathophysiology of certain diseases. Whereas specific RNA splicing events in pancreatic islets have been investigated in models of inflammation in vitro, how RNA splicing in the circulation correlates with or is reflective of type 1 diabetes (T1D) disease pathophysiology in humans remains unexplored. Objective: To use machine learning to investigate if alternative RNA splicing events differ between individuals with and without new-onset T1D and to determine if these splicing events provide insight into T1D pathophysiology. Methods: RNA deep sequencing was performed on whole blood samples from 2 independent cohorts: a training cohort consisting of 12 individuals with new-onset T1D and 12 age- and sex-matched nondiabetic controls and a validation cohort of the same size and demographics. Machine learning analysis was used to identify specific isoforms that could distinguish individuals with T1D from controls. Results: Distinct patterns of RNA splicing differentiated participants with T1D from unaffected controls. Notably, certain splicing events, particularly involving retained introns, showed significant association with T1D. Machine learning analysis using these splicing events as features from the training cohort demonstrated high accuracy in distinguishing between T1D subjects and controls in the validation cohort. Gene Ontology pathway enrichment analysis of the retained intron category showed evidence for a systemic viral response in T1D subjects. Conclusion: Alternative RNA splicing events in whole blood are significantly enriched in individuals with new-onset T1D and can effectively distinguish these individuals from unaffected controls. Further, our findings also suggest that RNA splicing profiles offer the potential to provide insights into disease pathogenesis.

60 APPLIED LIFE SCIENCES↗