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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.

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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2024

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Here, currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Efficient Optimization of Energy Recovery From Geothermal Reservoirs With Recurrent Neural Network Predictive Models

Improving the long-term energy production performance of geothermal reservoirs can be accomplished by optimizing field development and management plans. Reliable prediction models, however, are needed to evaluate and optimize the performance of the underlying reservoirs under various operation and development strategies. In traditional frameworks, physics-based simulation models are used to predict the energy production performance of geothermal reservoirs. However, detailed simulation models are not trivial to construct, require a reliable description of the reservoir conditions and properties, and entail high computational complexity. Data-driven predictive models can offer an efficient alternative for use in optimization workflows. This paper presents an optimization framework for net power generation in geothermal reservoirs using a variant of the recurrent neural network (RNN) as a data-driven predictive model. The RNN architecture is developed and trained to replace the simulation model for computationally efficient prediction of the objective function and its gradients with respect to the well control variables. The net power generation performance of the field is optimized by automatically adjusting the mass flow rate of production and injection wells over 12 years, using a gradient-based local search algorithm. Two field-scale examples are presented to investigate the performance of the developed data-driven prediction and optimization framework. Furthermore, the prediction and optimization results from the RNN model are evaluated through comparison with the results obtained by using a numerical simulation model of a real geothermal reservoir.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

Learning to Simulate Aerosol Dynamics with Graph Neural Networks

Aerosol effects on climate, weather, and air quality depend on characteristics of individual particles, which are tremendously diverse and change in time. Particle-resolved models are the only models able to capture this diversity in particle physiochemical properties, and these models are computationally expensive. As a strategy for accelerating particle-resolved microphysics models, we introduce Graph-based Learning of Aerosol Dynamics (GLAD) and use this model to train a surrogate of the particle-resolved model PartMC-MOSAIC. GLAD implements a Graph Network-based Simulator (GNS), a machine learning framework that has been used to simulate particle-based fluid dynamics models. In GLAD, each particle is represented as a node in a graph, and the evolution of the particle population over time is simulated through learned message passing. Here, we demonstrate our GNS approach on a simple aerosol system that includes condensation of sulfuric acid onto particles composed of sulfate, black carbon, organic carbon, and water. A graph with particles as nodes is constructed, and a graph neural network (GNN) is then trained using the model output from PartMC-MOSAIC. The trained GNN can then be used for simulating and predicting aerosol dynamics over time. Results demonstrate the framework's ability to accurately learn chemical dynamics and generalize across different scenarios, achieving efficient training and prediction times. We evaluate the performance across four scenarios, highlighting the framework's robustness and adaptability in modeling aerosol microphysics and chemistry.

aerosol chemistry dynamics↗
DOE OSTI2026

Patch-Based Convolutional Neural Networks for Multiple Microstructural Features Detection in FIB-SEM Micrographs of Irradiated Nuclear Fuel

Focused ion beam scanning electron microscopy (FIB-SEM) tomography has increasingly been utilized for acquiring three-dimensional (3D) microstructure features at the sub-micron scale in irradiated nuclear materials. This technique involves sequential ion beam slicing followed by electron beam imaging and compositional mapping using energy dispersive spectroscopy (EDS). Despite its growing use, several challenges persist. These include the time-intensive nature of data collection of EDS data, difficulties in distinguishing between various microstructures, and issues with image alignment. These challenges currently limit the broader application of FIB-SEM tomography in the field. To overcome these limitations, we propose using convolutional neural networks (CNNs) to automate microstructure identification in SEM images. Our study introduces a new framework for identifying microstructures in irradiated U-10Zr (wt. %) metallic fuel with limited annotated data. The framework includes the creation of a reliable annotated dataset with paired SEM and ground truth data from EDS maps, the applications of CNNs for microstructure identification, and the validation of model performance. Specifically, we employed the Segment Anything Model (SAM) to align SEM images with corresponding EDS maps and focused ion beam (FIB) tomography SEM data. We evaluate several models, including Patch-based U-Net, Attention U-Net, and Residual U-Net, finding that patch-based U-Net exhibits superior segmentation performance and consistency. This approach reduces reliance on EDS detectors and aids in accelerating nuclear material analysis process, highlighting the potential of advanced deep learning techniques to improve microstructural understanding in nuclear material. This is the first framework to integrate SAM and Patch-based CNN models for semantic segmentation of irradiated nuclear materials, with potential applicability to other tomography datasets.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

Thermodynamic Modeling of Complex Solid Solutions in the Lu-H-N System via Graph Neural Network Accelerated Monte Carlo Simulations

Metal hydrides are important across diverse applications, such as hydrogen storage, batteries, gas sensors, nuclear reactions, and high-temperature superconductivity. Previous computational studies of metal hydrides under extreme pressures, e.g., 𝑂⁡(10 2 ) ⁢GPa, usually treat them as stoichiometric compounds without considering interstitial lattice disorder. As pressures become more moderate in the 𝑂⁡(10 0 ) ⁢GPa and below range, hydrogen disorder at interstitial lattice sites becomes prominent, e.g., in the N-doped Lu hydride that was recently claimed superconducting near 1 GPa. Further adding compositional complexity from alloying and/or multielement interstitial occupation makes elucidating pressure- and temperature-dependent observables intractable by first-principles calculations alone. We therefore propose a lattice graph neural-network surrogate modeling approach to predict configuration- and pressure-dependent equation-of-state properties. Their efficiency permits Monte Carlo simulations to calculate Gibbs energies and pressure-dependent phase diagrams, thereby revealing insights into the synthesis conditions required for achieving desired phase equilibria. We demonstrate this concept for the compositionally complex cubic Lu(H,N,Va) 3 system where three constituents (hydrogen, nitrogen and vacancy) have disordered multielement interstitial occupancies and insights into pressure-dependent phase equilibria are critically needed, e.g., N-doping levels can significantly lower dehydrogenation temperatures and provide a new strategy to optimize hydrogen-storage alloys. This work can improve the thermodynamic understanding of the Lu-H-N system and help rational synthesis of N-doped Lu hydrides, but more generally demonstrates an efficient approach to model pressure-dependent thermodynamics of multicomponent solid solutions.

Monte Carlo methods↗
DOE OSTI2024

Utah FORGE 6-3712: Probabilistic Estimation of Seismic Response Using Physics-Informed Recurrent Neural Networks - 2024 Annual Workshop Presentation

This is a presentation on the Probabilistic Estimation of Seismic Response Using Physics-Informed Recurrent Neural Networks by GTC Analytics, presented by Jesse Williams. This video slide presentation discusses the development of machine learning-based predictive tools to estimate the magnitude-frequency response of stimulation-induced seismicity. This presentation was featured in the Utah FORGE R&D Annual Workshop on August 15, 2024.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

One-shot gas detection with transformer paired neural networks in Mako collected longwave infrared hyperspectral imagery

To date, careful data treatment workflows and statistical detectors are used to perform hyperspectral image (HSI) detection of any gas contained in a spectral library, which is often expanded with physics models to incorporate different spectral characteristics. In general, surrounding evidence or known gas-release parameters are used to provide confidence in or confirm detection capability, respectively. This makes quantifying detection performance difficult as it is nearly impossible to develop an absolute ground truth for gas target pixel presence in collected HSI. Consequently, developing and comparing new detection methods, especially machine learning (ML)-based methods, is susceptible to subjectivity in derived detection map quality. Here, in this work, we demonstrate the first use of transformer-based paired neural networks (PNNs) for one-shot gas target detection for multiple gases while providing quantitative classification and detection metrics for their use on labeled data. Terabytes of training data are generated from a database of long-wave infrared HSI obtained from historical Mako sensor campaigns over Los Angeles. By incorporating labels, singular signature representations, and a model development pipeline, we can tune and select PNNs to detect multiple gas targets that are not seen in training on a quantitative basis. We additionally assess our test set detections using interpretability techniques widely employed with ML-based predictors, but less common with detection methods relying on learned latent spaces.

Hyperspectral imaging↗
DOE OSTI2022

Implementing Spatio-Temporal 3D-Convolution Neural Networks and UAV Time Series Imagery to Better Predict Lodging Damage in Sorghum

Unmanned aerial vehicle (UAV)-based remote sensing is gaining momentum in a variety of agricultural and environmental applications. Very-high-resolution remote sensing image sets collected repeatedly throughout a crop growing season are becoming increasingly common. Analytical methods able to learn from both spatial and time dimensions of the data may allow for an improved estimation of crop traits, as well as the effects of genetics and the environment on these traits. Multispectral and geometric time series imagery was collected by UAV on 11 dates, along with ground-truth data, in a field trial of 866 genetically diverse biomass sorghum accessions. We compared the performance of Convolution Neural Network (CNN) architectures that used image data from single dates (two spatial dimensions, 2D) versus multiple dates (two spatial dimensions + temporal dimension, 3D) to estimate lodging detection and severity. Lodging was detected with 3D-CNN analysis of time series imagery with 0.88 accuracy, 0.92 Precision, and 0.83 Recall. This outperformed the best 2D-CNN on a single date with 0.85 accuracy, 0.84 Precision, and 0.76 Recall. The variation in lodging severity was estimated by the best 3D-CNN analysis with 9.4% mean absolute error (MAE), 11.9% root mean square error (RMSE), and goodness-of-fit (R2) of 0.76. This was a significant improvement over the best 2D-CNN analysis with 11.84% MAE, 14.91% RMSE, and 0.63 R2. The success of the improved 3D-CNN analysis approach depended on the inclusion of “before and after” data, i.e., images collected on dates before and after the lodging event. The integration of geometric and spectral features with 3D-CNN architecture was also key to the improved assessment of lodging severity, which is an important and difficult-to-assess phenomenon in bioenergy feedstocks such as biomass sorghum. This demonstrates that spatio-temporal CNN architectures based on UAV time series imagery have significant potential to enhance plant phenotyping capabilities in crop breeding and Precision agriculture applications.

3D-convolution neural networks↗
DOE OSTI2023

Artificial Neural Network Models for Octane Number and Octane Sensitivity: A Quantitative Structure Property Relationship Approach to Fuel Design

Octane sensitivity (OS), defined as the research octane number (RON) minus the motor octane number (MON) of a fuel, has gained interest among researchers due to its effect on knocking conditions in internal combustion engines. Compounds with a high OS enable higher efficiencies, especially within advanced compression ignition engines. RON/MON must be experimentally tested to determine OS, requiring time, funding, and specialized equipment. Thus, predictive models trained with existing experimental data and molecular descriptors (via quantitative structure-property relationships (QSPRs)) would allow for the preemptive screening of compounds prior to performing these experiments. Here, the present work proposes two methods for predicting the OS of a given compound: using artificial neural networks (ANNs) trained with QSPR descriptors to predict RON and MON individually to compute OS (derived octane sensitivity (dOS)), and using ANNs trained with QSPR descriptors to directly predict OS. Twenty-five ANNs were trained for both RON and MON and their test sets achieved an overall 6.4% and 5.2% error, respectively. Twenty-five additional ANNs were trained for both dOS and OS; dOS calculations were found to have 15.3% error while predicting OS directly resulted in 9.9% error. A chemical analysis of the top QSPR descriptors for RON/MON and OS is conducted, highlighting desirable structural features for high-performing molecules and offering insight into the inner mathematical workings of ANNs; such chemical interpretations study the interconnections between structural features, descriptors, and fuel performance showing that connectivity, structural diversity, and atomic hybridization consistently drive fuel performance.

09 BIOMASS FUELS↗
DOE OSTI2024

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. Here, we present a spectral decomposition method that allows for corrections to line positions and bound–bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Deep Convolutional Neural Networks Exploit High-Spatial- and -Temporal-Resolution Aerial Imagery to Phenotype Key Traits in Miscanthus

Miscanthus is one of the most promising perennial crops for bioenergy production, with high yield potential and a low environmental footprint. The increasing interest in this crop requires accelerated selection and the development of new screening techniques. New analytical methods that are more accurate and less labor-intensive are needed to better characterize the effects of genetics and the environment on key traits under field conditions. We used persistent multispectral and photogrammetric UAV time-series imagery collected 10 times over the season, together with ground-truth data for thousands of Miscanthus genotypes, to determine the flowering time, culm length, and biomass yield traits. We compared the performance of convolutional neural network (CNN) architectures that used image data from single dates (2D-spatial) versus the integration of multiple dates by 3D-spatiotemporal architectures. The ability of UAV-based remote sensing to rapidly and non-destructively assess large-scale genetic variation in flowering time, height, and biomass production was improved through the use of 3D-spatiotemporal CNN architectures versus 2D-spatial CNN architectures. The performance gains of the best 3D-spatiotemporal analyses compared to the best 2D-spatial architectures manifested in up to 23% improvements in R2, 17% reductions in RMSE, and 20% reductions in MAE. The integration of photogrammetric and spectral features with 3D architectures was crucial to the improved assessment of all traits. In conclusion, our findings demonstrate that the integration of high-spatiotemporal-resolution UAV imagery with 3D-CNNs enables more accurate monitoring of the dynamics of key phenological and yield-related crop traits. This is especially valuable in highly productive, perennial grass crops such as Miscanthus, where in-field phenotyping is especially challenging and traditionally limits the rate of crop improvement through breeding.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Efficient mapping between void shapes and stress fields using Deep Convolutional Neural Networks with sparse data

Establishing fast and accurate structure-to-property relationships is an important component in the design and discovery of advanced materials. Physics-based simulation models like the finite element method (FEM) are often used to predict deformation, stress, and strain fields as a function of material microstructure in material and structural systems. Such models may be computationally expensive and time intensive if the underlying physics of the system is complex. This limits their application to solve inverse design problems and identify structures that maximize performance. In such scenarios, surrogate models are employed to make the forward mapping computationally efficient to evaluate. However, the high dimensionality of the input microstructure and the output field of interest often renders such surrogate models inefficient, especially when dealing with sparse data. Deep convolutional neural network (CNN) based surrogate models have shown great promise in handling such high-dimensional problems. In this paper, a single ellipsoidal void structure under a uniaxial tensile load represented by a linear elastic, high-dimensional and expensive-to-query, FEM model. We consider two deep CNN architectures, a modified convolutional autoencoder framework with a fully connected bottleneck and a UNet CNN, and compare their accuracy in predicting the von Mises stress field for any given input void shape in the FEM model. Additionally, a sensitivity analysis study is performed using the two approaches, where the variation in the prediction accuracy on unseen test data is studied through numerical experiments by varying the number of training samples from 20 to 100.

surrogate modeling; convolutional neural networks;↗
DOE OSTI2022

Physics-Informed Neural Network Modeling of Li-Ion Batteries: Preprint

Li-ion batteries (LIB) are a promising solution to enable storage of intermittent energy sources due to their high energy density. However, LIBs are known to significantly degrade after about 1000 charge-discharge cycles. LIBs degrade following different degradation modes and at a rate that depends on the operating conditions (external temperature, load). To plan the installation of batteries, appropriate understanding and prediction capabilities of their lifecycle is needed. High-fidelity numerical models of LIBs such as the pseudo-two-dimensional (P2D) model have been shown to accurately represent the charge-discharge-cycle of an LIB given ac- curate choice of the physical parameters. Given the large number of P2D parameters, adjusting them using forward runs is intractable. This work describes the development of a physics-informed neural network (PINN) as a surrogate substitute of the P2D model that captures parameter dependence. The PINN is advantageous as it needs little to no data, and can naturally encode the dependence of every model parameter. Here, a specific training procedure is adopted to efficiently cover parameter space, handle model stiffness and enforce boundary conditions. The trained PINN is validated against numerical solutions of the P2D model, and its applicability to battery degradation modeling is discussed.

battery degradation↗
DOE OSTI2022

Data reduction through optimized scalar quantization for more compact neural networks

Raw data generation for several existing and planned large physics experiments now exceeds TB/s rates, generating untenable data sets in very little time. Those data often demonstrate high dimensionality while containing limited information. Meanwhile, Machine Learning algorithms are now becoming an essential part of data processing and data analysis. Those algorithms can be used offline for post processing and post data analysis, or they can be used online for real time processing providing ultra low latency experiment monitoring. Both use cases would benefit from data throughput reduction while preserving relevant information: one by reducing the offline storage requirements by several orders of magnitude and the other by allowing ultra fast online inferencing with low complexity Machine Learning models. Moreover, reducing the data source throughput also reduces material cost, power and data management requirements. In this work we demonstrate optimized nonuniform scalar quantization for data source reduction. This data reduction allows lower dimensional representations while preserving the relevant information of the data, thus enabling high accuracy Tiny Machine Learning classifier models for online fast inferences. We demonstrate this approach with an initial proof of concept targeting the CookieBox, an array of electron spectrometers used for angular streaking, that was developed for LCLS-II as an online beam diagnostic tool. We used the Lloyd-Max algorithm with the CookieBox dataset to design an optimized nonuniform scalar quantizer. Optimized quantization lets us reduce input data volume by 69% with no significant impact on inference accuracy. When we tolerate a 2% loss on inference accuracy, we achieved 81% of input data reduction. Finally, the change from a 7-bit to a 3-bit input data quantization reduces our neural network size by 38%.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Monitoring of Liquid Metal Reactor Heater Zones with Recurrent Neural Network Learning of Temperature Time Series

Advanced high-temperature fluid reactors (ARs), such as sodium fast reactors (SFRs) and molten salt cooled reactors (MSCRs) utilize high-temperature fluids at ambient pressure. To melt the fluid during reactor startup and prevent fluid freezing during cooldown, the thermal–hydraulic systems of such ARs include heater zones consisting of specific heaters with controllers, temperature sensors, and thermal insulation. The failure of heater zones due to insulation material degradation or improper installation, resulting in parasitic heat losses, can lead to fluid freezing. The detection of faults using a heat-transfer model is difficult because of a lack of knowledge of the experimental details. Data-driven machine learning of heater zone temperature time series offers a viable alternative. In this study, we benchmarked the performance of recurrent neural networks (RNNs) in an analysis of heat-up transient temperature time series of heater zones installed on a liquid sodium vessel. The RNN models include long short-term memory (LSTM) and gated recurrent unit (GRU) networks, as well as their bi-directional variants, BiLSTM and BiGRU. Anomalous temperature points were designated using a percentile-based threshold applied to residual fluctuations in the detrended temperature time series. Additionally, the impact of the exponentially weighted moving average (EWMA) method on detection accuracy was examined. The RNN models’ performance was assessed using precision, recall, and F 1 score metrics. Results demonstrated that RNN models effectively detect anomalies in temperature time series with the best models for each heater zone achieving F 1 scores of over 93%. To explain the variations in RNN model performance across different heater zones, we used Kullback–Leibler (KL) divergence to quantify the relative entropy between training and testing data, and the Detrended Fluctuation Analysis (DFA) to assess long-range temporal correlations. For datasets with strong long-range correlations and minimal relative entropy between training and testing data, GRU is the best-performing model. When the data exhibits weaker long-term correlations and a significant relative entropy between training and testing distributions, BiGRU shows the best performance. For the data sets with intermediate values of both KL divergence and DFA, the best performance is obtained with LSTM and BiLSTM, respectively.

gated recurrent unit↗
DOE OSTI2022

End-to-end optimization for battery materials and molecules by combining graph neural networks and reinforcement learning

The National Renewable Energy Laboratory (NREL), together with the Colorado School of Mines (CSM) and Colorado State University (CSU), has developed a machine learning-enhanced approach to design new battery materials. Currently, such materials are designed in part via numerous expensive high-fidelity computational simulations that predict the performance of a given composition. Even with computational screening tools, the vast landscape of possible molecular or crystal structures exceeds current and future computational capacity. Improving the efficiency by which new materials can be optimized will therefore disrupt the cost, risk, and time required to bring new energy solutions to the marketplace. Predicting the properties of an organic molecule or periodic crystalline material given its structure has grown increasingly common. These approaches leverage large-scale computational and experimental databases and ML approaches such as graph neural networks. The inverse design problem of finding a material that possesses desired properties is substantially more challenging, since enumerating all valid material structures is not feasible. In this project, we leveraged recent success in reinforcement learning to efficiently navigate this high-dimensional search space. Just as algorithms can find the optimal chess moves from nearly limitless options, we train an approach to evolve a simple starting structure into a complex structure that possess the desired properties. Our solution has been demonstrated by applying it to two related design application tasks for short- and long-term energy storage, respectively: (1) the design of solid-state ion conductors and (2) the design of organic redox-active materials. The project has resulted an open-source software library for material design, documented examples of applying the library to both organic and inorganic material optimization, and peer-reviewed publications detailing the data, computational models, and resulting candidate materials.

25 ENERGY STORAGE↗
DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗