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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Updates of Land Surface and Air Quality Products in NASA MAIRS and NEESPI Data Portals

Following successful support of the Northern Eurasia Earth Sciences Partner Initiative (NEESPI) project with NASA satellite remote sensing data, from Spring 2009 the NASA GES DISC (Goddard Earth Sciences Data and Information Services Center) has been working on collecting more satellite and model data to support the Monsoon Asia Integrated Regional Study (MAIRS) project. The established data management and service infrastructure developed for NEESPI has been used and improved for MAIRS support.Data search, subsetting, and download functions are available through a single system. A customized Giovanni system has been created for MAIRS.The Web-based on line data analysis and visualization system, Giovanni (Goddard Interactive Online Visualization ANd aNalysis Infrastructure) allows scientists to explore, quickly analyze, and download data easily without learning the original data structure and format. Giovanni MAIRS includes satellite observations from multiple sensors and model output from the NASA Global Land Data Assimilation System (GLDAS), and from the NASA atmospheric reanalysis project, MERRA. Currently, we are working on processing and integrating higher resolution land data in to Giovanni, such as vegetation index, land surface temperature, and active fire at 5km or 1km from the standard MODIS products. For data that are not archived at the GESDISC,a product metadata portal is under development to serve as a gateway for providing product level information and data access links, which include both satellite, model products and ground-based measurements information collected from MAIRS scientists.Due to the large overlap of geographic coverage and many similar scientific interests of NEESPI and MAIRS, these data and tools will serve both projects.

Shen, Suhung↗
DOE OSTI2023

Developing machine-learning potentials to study properties of the tritium formation and diffusivity in pure and defective Zircaloy-4 getters

Objective of this work was to study the formation of Sn impurity and hydride phases in Zr and study their impacts on the diffusion kinetics of 3 H by using DFT based ML approach. By implementing deep neural potential (DNP) technique, we developed potential for Zr-H and Sn impurity systems and validated the DNP by using DFT results. We found that by implementing machine learning approach, it is possible to achieve accuracy comparable to DFT level for the more realistic models by using less computational time and resources.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Cognitive IoT and Edge Computing for Intrusion Detection with Federated TinyML

Internet of Things (IoT) and Edge Computing (EC) are rapidly becoming an integral part of the modern society. By 2030, there is estimated to be over 40 billion active and connected IoT devices [1]. This rapid progress also comes with a significant implication on cybersecurity. Back-end infrastructure and systems have a much broader attack than they did previously due to vulnerable IoT/EC devices being connected to wireless networks. This expanding attack surface is a growing concern because IoT/EC are increasingly being used in critical systems such as power grids, health care, and smart homes. To effectively address a problem of this scale, cognitive cyber methods—which can autonomously detect and react to cyber attacks as they develop—are needed. To address this, we bring Artificial Intelligence (AI) and Machine Learning (ML) to IoT/EC devices, using tinyML to monitor voluminous IoT data against cyber threats, and using Federated Learning (FL) to share local detection knowledge across the system while preserving privacy. We propose a novel three-layer architecture: (1) an IoT layer for tinyML-based inference, (2) an edge layer for ML model training, and (3) a cloud layer for FL operations. Using the publicly available 11-class N-BaIoT dataset [2], we demonstrate that this architecture mitigates resource constraints at the IoT layer while improving detection accuracy over standard two-layer designs. An outlier-resistant scaler, feature reduction, and quantization enable the tinyML model to maintain detection accuracy with a reduced model size. Additionally, federated learning that only utilizes the intersection (across heterogenous devices) of the reduced feature set achieves superior detection accuracy compared to locally trained models.

Li, Mingyan [ORNL] (ORCID:0009000569532640)↗
DOE OSTI2023

Deep learning integrates histopathology and proteogenomics at a pan-cancer level

We introduce a pioneering approach that integrates pathology imaging with transcriptomics and proteomics to identify predictive histology features associated with critical clinical outcomes in cancer. We utilize 2,755 H&E-stained histopathological slides from 657 patients across 6 cancer types from CPTAC. Our models effectively recapitulate distinctions readily made by human pathologists: tumor vs. normal (AUROC = 0.995) and tissue-of-origin (AUROC = 0.979). We further investigate predictive power on tasks not normally performed from H&E alone, including TP53 prediction and pathologic stage. Importantly, we describe predictive morphologies not previously utilized in a clinical setting. The incorporation of transcriptomics and proteomics identifies pathway-level signatures and cellular processes driving predictive histology features. Model generalizability and interpretability is confirmed using TCGA. We propose a classification system for these tasks, and suggest potential clinical applications for this integrated human and machine learning approach. A publicly available web-based platform implements these models.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Improving Spectral Resolution from Real-time Evolution for Correlated Systems

Abstract The quality of numerically simulated spectra using real-time evolution methods for strongly correlated systems is affected by both the length of simulation time and the system size, limiting resolution in both frequency and momentum. In this work, we propose a computationally cheap, linear autoregressive machine learning-based framework to extend short-time and short-distance results over a wider range. We use the proposed method to extend the lesser Green’s function for both the Hubbard model and the much more computationally challenging Hubbard-extended Holstein model. This technique significantly improves both the frequency and momentum resolution of the single-particle removal spectrum $${\mathcal{A}}(k,\omega )$$ A ( k , ω ) , allowing the observation of otherwise obscured spectral features due to electron-phonon coupling.

Tang, Ta↗
DOE OSTI2022

Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Introducing the DREAMS Project: DaRk mattEr and Astrophysics with Machine Learning and Simulations

We introduce the DaRk mattEr and Astrophysics with Machine learning and Simulations (DREAMS) project, an innovative approach to understanding the astrophysical implications of alternative dark matter (DM) models and their effects on galaxy formation and evolution. The DREAMS project will ultimately comprise thousands of cosmological hydrodynamic simulations that simultaneously vary over DM physics, astrophysics, and cosmology in modeling a range of systems—from galaxy clusters to ultra-faint satellites. Such extensive simulation suites can provide adequate training sets for machine-learning-based analyses. This paper introduces two new cosmological hydrodynamical suites of warm dark matter (WDM), each comprising 1024 simulations generated using the arepo code. One suite consists of uniform-box simulations covering a ${(25\,{h}^{-1}\,{\rm{Mpc}})}^{3}$ volume, while the other consists of Milky Way zoom-ins with sufficient resolution to capture the properties of classical satellites. For each simulation, the WDM particle mass is varied along with the initial density field and several parameters controlling the strength of baryonic feedback within the IllustrisTNG model. We provide two examples, separately utilizing emulators and convolutional neural networks, to demonstrate how such simulation suites can be used to disentangle the effects of DM and baryonic physics on galactic properties. The DREAMS project can be extended further to include different DM models, galaxy formation physics, and astrophysical targets. In this way, it will provide an unparalleled opportunity to characterize uncertainties on predictions for small-scale observables, leading to robust predictions for testing the particle physics nature of DM on these scales.

cosmological parameters↗
NASA NTRS2005

Upper Torso Control for HOAP-2 Using Neural Networks

Humanoid robots have similar physical builds and motion patterns as humans. Not only does this provide a suitable operating environment for the humanoid but it also opens up many research doors on how humans function. The overall objective is replacing humans operating in unsafe environments. A first target application is assembly of structures for future lunar-planetary bases. The initial development platform is a Fujitsu HOAP-2 humanoid robot. The goal for the project is to demonstrate the capability of a HOAP-2 to autonomously construct a cubic frame using provided tubes and joints. This task will require the robot to identify several items, pick them up, transport them to the build location, then properly assemble the structure. The ability to grasp and assemble the pieces will require improved motor control and the addition of tactile feedback sensors. In recent years, learning-based control is becoming more and more popular; for implementing this method we will be using the Adaptive Neural Fuzzy Inference System (ANFIS). When using neural networks for control, no complex models of the system must be constructed in advance-only input/output relationships are required to model the system.

Sandoval, Steven P.↗
NASA NTRS2009

Finite-difference simulation and visualization of elastodynamics in time-evolving generalized curvilinear coordinates

Modeling and simulation of free and forced structural vibrations is essential to an overall structural health monitoring capability. In the various embodiments, a first principles finite-difference approach is adopted in modeling a structural subsystem such as a mechanical gear by solving elastodynamic equations in generalized curvilinear coordinates. Such a capability to generate a dynamic structural response is widely applicable in a variety of structural health monitoring systems. This capability (1) will lead to an understanding of the dynamic behavior of a structural system and hence its improved design, (2) will generate a sufficiently large space of normal and damage solutions that can be used by machine learning algorithms to detect anomalous system behavior and achieve a system design optimization and (3) will lead to an optimal sensor placement strategy, based on the identification of local stress maxima all over the domain.

Kaul, Upender K.↗
NASA NTRS2016

An Integrated Gate Turnaround Management Concept Leveraging Big Data Analytics for NAS Performance Improvements

"Gate Turnaround" plays a key role in the National Air Space (NAS) gate-to-gate performance by receiving aircraft when they reach their destination airport, and delivering aircraft into the NAS upon departing from the gate and subsequent takeoff. The time spent at the gate in meeting the planned departure time is influenced by many factors and often with considerable uncertainties. Uncertainties such as weather, early or late arrivals, disembarking and boarding passengers, unloading/reloading cargo, aircraft logistics/maintenance services and ground handling, traffic in ramp and movement areas for taxi-in and taxi-out, and departure queue management for takeoff are likely encountered on the daily basis. The Integrated Gate Turnaround Management (IGTM) concept is leveraging relevant historical data to support optimization of the gate operations, which include arrival, at the gate, departure based on constraints (e.g., available gates at the arrival, ground crew and equipment for the gate turnaround, and over capacity demand upon departure), and collaborative decision-making. The IGTM concept provides effective information services and decision tools to the stakeholders, such as airline dispatchers, gate agents, airport operators, ramp controllers, and air traffic control (ATC) traffic managers and ground controllers to mitigate uncertainties arising from both nominal and off-nominal airport gate operations. IGTM will provide NAS stakeholders customized decision making tools through a User Interface (UI) by leveraging historical data (Big Data), net-enabled Air Traffic Management (ATM) live data, and analytics according to dependencies among NAS parameters for the stakeholders to manage and optimize the NAS performance in the gate turnaround domain. The application will give stakeholders predictable results based on the past and current NAS performance according to selected decision trees through the UI. The predictable results are generated based on analysis of the unique airport attributes (e.g., runway, taxiway, terminal, and gate configurations and tenants), and combined statistics from past data and live data based on a specific set of ATM concept-of-operations (ConOps) and operational parameters via systems analysis using an analytic network learning model. The IGTM tool will then bound the uncertainties that arise from nominal and off-nominal operational conditions with direct assessment of the gate turnaround status and the impact of a certain operational decision on the NAS performance, and provide a set of recommended actions to optimize the NAS performance by allowing stakeholders to take mitigation actions to reduce uncertainty and time deviation of planned operational events. An IGTM prototype was developed at NASA Ames Simulation Laboratories (SimLabs) to demonstrate the benefits and applicability of the concept. A data network, using the System Wide Information Management (SWIM)-like messaging application using the ActiveMQ message service, was connected to the simulated data warehouse, scheduled flight plans, a fast-time airport simulator, and a graphic UI. A fast-time simulation was integrated with the data warehouse or Big Data/Analytics (BAI), scheduled flight plans from Aeronautical Operational Control AOC, IGTM Controller, and a UI via a SWIM-like data messaging network using the ActiveMQ message service, illustrated in Figure 1, to demonstrate selected use-cases showing the benefits of the IGTM concept on the NAS performance.

Efficent ATM systems↗
NASA NTRS2019

Health Management and Prognostics for Electric Aircraft Powertrain

W and c Any air borne vehicle needs incorporating safety as key parameter of measure, and inclusion of autonomy raises the critical need for safety under autonomous operations. Management of faults and component degradation is key as complexity in autonomous operations grow over the period of time. Therefore, in addition to basic operational requirements, an autonomous electric vehicle should be able to make accurate estimates of its current system health and take the correct decisions to complete its mission successfully. Real-time safety and state-awareness tools are therefore essential for the vehicle to be able to reach its destination in a safe and successful manner. The need for safety assurance and health management capabilities is particularly relevant for aircraft electric propulsion systems, which are relatively new and with limited historical to learn. They are critical systems requiring high power density along with reliability, resilience, efficient management of weight, and operational costs. A model- based fault diagnosis and prognostics approach of complex critical systems can successfully accomplish the safety and state awareness goal for such electric propulsion systems, enabling autonomous decision making capability for safe and efficient operation. To identify critical components in the system a Qualitative Bayesian approach using FMECA is implemented. This requires the assessment of some quantities representing the state of the electric unmanned aerial systems (e-UAS), as well as look-ahead forecasts of such states during the entire flight, presented in form of safety metrics (SM). In-service data and performance data gathered from degraded components sup- ports diagnostic and prognostic methods for these systems, but this data can be difficult to obtain as weight and packaging restrictions reduce redundancy and instrumentation on-board the vehicle. Therefore, an model-based framework should be capable or operating with limited data. In addition to data scarcity, the variability of such complex critical systems re- quires the model-based framework to reason in the presence of uncertainty, such as sensor noise, and modeling imperfections. Quantification of errors and uncertainties in the measured states and quantities is therefore a fundamental step for a precise estimation of such SMs; un-modeled uncertainty may result in erroneous state assessment and un- reliable predictions of future states of e-UAVs. Typical, centralized model-based schemes suffer from inherent disadvantages such as computational complexity, single point of failure, and scalability issues, and therefore may fail in such a complex scenario. This paper presents a methodology for developing a system level diagnostics and prognostics approach using a Qualitative Bayesian FMECA approach along with a formal uncertainty management framework for an e-UAS. In this work we demonstrate the efficacy of the framework to predict effects of sub-system level degradation on vehicle operation incorporating uncertainty management to predict future behavior under different operating conditions.

Kulkarni, Chetan↗
DOE OSTI2021

A Machine Learning-Based Method to Estimate Transformer Primary-Side Voltages with Limited Customer-Side AMI Measurements: Preprint

Distribution control applications such as volt/var optimization, network reconfiguration, and distribution automation require accurate knowledge of the distribution system state. The lack of sufficient sensors on the primary side of distribution networks often limits the accuracy of the control decisions by these applications. The deployment of advanced metering infrastructure (AMI) provides utilities an opportunity to translate the AMI data on the secondary onto the primary so that it can be used as pseudo-measurements to augment the limited existing measurements on the primary. This paper develops an approach for estimating service transformer primary-side voltages by using limited secondary-side AMI measurements. The estimated primary-side voltages can be used by utilities as pseudo-measurements for distribution control applications. The detailed secondary model topology, which is an essential input data for many existing algorithms, is not required for the proposed method. The performance of the proposed method is validated by using AMI measurements from the field and an actual distribution feeder model of San Diego Gas & Electric Company.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Toward designing effective exascale scientific computing workflows: experiences and best practices

Many fields within scientific computing have embraced advances in big-data analysis and machine learning, which often requires the deployment of large, distributed and complicated workflows that may combine training neural networks, performing simulations, running inference, and performing database queries and data analysis in asynchronous, parallel and pipelined execution frameworks. Such a shift has brought into focus the need for scalable, efficient workflow management solutions with reproducibility, error and provenance handling, traceability, and checkpoint-restart capabilities, among other needs. Here, we discuss challenges and best-practices for deploying exascale-generation computational science workflows on resources at the Oak Ridge Leadership Computing Facility (OLCF). We present our experiences with large-scale deployment of distributed workflows on the Summit supercomputer, including for bioinformatics and computational biophysics, materials science, and deep learning model optimization. We also present problems and solutions created by working within a Python-centric software base on traditional HPC systems, and discuss steps that will be required before the convergence of HPC, AI, and data science can be fully realized. Our results point to a wealth of exciting new possibilities for harnessing this convergence to tackle new scientific challenges.

Coletti, Mark↗
NASA NTRS2022

Event Report for The Ethical Artificial Intelligence Quantification Workshop

Artificial Intelligence (AI) is a powerful emerging technology area which requires special attention to using it ethically. AI ethics is still an emerging field, and the partners for this workshop and report seek to move AI ethics discussion ahead by experimenting with ways to measure AI ethics criteria. The following document describes the outcomes and learnings from The Ethical Artificial Intelligence Quantification Workshop held at the National Institute for Aerospace (NIA), Hampton, Virginia on May 12th, 2022. The purpose of the workshop was for participants to evaluate and experiment-with the methodology and process presented by AIEthics.World in cooperation with Intel Corporation. The meeting participants learned about the Ethical AI Certification and Maturity Model™ and applied the methodology to selected notional AI systems. The workshop facilitated the evaluation of the maturity of the AI system according to ethical considerations relevant to NASA, NIA and other participants. The workshop consisted of three main phases. The first phase focused on understanding and summarizing NASA’s ethical approaches, mission and values based on published documentation, discussions and individual insights & opinions of participants. This information was prioritized, weighted, ordered, and quantified in phase two, to formulate an alignment between human values (ethics) and their applicability to AI systems during all lifecycle phases. The first two phases were summarized as a form of ethical genealogy for artificial intelligence, specific to NASA’s ethical approaches. In the third and last phase of the workshop the participants evaluated notional examples of artificial intelligence to qualify and quantify its ability to adhere to the organizational ethics approaches, using the Ethical AI Certification and Maturity Model™. The workshop uses the concept of genealogy, in the traditional sense: the study and traceability of lines of ancestors in the process of evolutionary development from earlier forms. However, as it is applied to an Ethical AI definition, it is providing the insights to the necessary and mandatory traceability of content, data, metrics, telemetry, elements, and structures which are used in the AI’s lifecycle to foster and measure AI ethics in all steps of its lifecycle. The Ethical Artificial Intelligence Quantification Workshop provided NASA with the opportunity to apply the Ethical AI Certification and Maturity Model™, in combination with existing and well-known decision-making and quality control methods to identify the metrics and measurements for an Ethical AI and assess its ethical condition and quality aligned with NASA ethics approaches. The result of the workshop is the capacity for NASA to apply the maturity model assessment to its AI Systems as desired and if necessary, publish the ability of these AI Systems to adhere to the organizational ethical goals. AI ethics frameworks need to be customized for each application domain, for example, individual NASA Mission Directorates. General principles that work in one area such as AI/Machine Learning-based text analysis (the ethics of information-extraction) may need to be adapted for another such as sense-and-avoid decision-making in a flight environment. The workshop was conducted among approximately twenty NASA subject matter experts, so the elements noted above should be considered examples, not definitive NASA ethical AI principles, genealogy, etc. Generating a definitive AI ethics framework for an organization as diverse as NASA would require far more discussion, debate, review, etc. However, the workshop provided valuable insight into mechanisms and processes for quantifying AI ethical qualities.

Artificial Intelligence↗
DOE OSTI2025

HAMscope: a snapshot Hyperspectral Autofluorescence Miniscope for real-time molecular imaging

We introduce HAMscope, a compact, snapshot hyperspectral autofluorescence miniscope that enables real-time, label-free molecular imaging in a wide range of biological systems. By integrating a thin polymer diffuser into a widefield miniscope, HAMscope spectrally encodes each frame and employs a probabilistic deep learning framework to reconstruct 30-channel hyperspectral stacks (452-703 nm) or directly infer molecular composition maps from single images. A scalable multi-pass U-Net architecture with transformer-based attention and per pixel uncertainty estimation enables high spatio-spectral fidelity (mean absolute error ∼0.0048) at video rates. While initially demonstrated in plant systems, including lignin, chlorophyll, and suberin imaging in intact poplar and cork tissues, the platform is readily adaptable to other applications such as neural activity mapping, metabolic profiling, and histopathology. We show that the system generalizes to out-of-distribution tissue types and supports direct molecular mapping without the need for spectral unmixing. HAMscope establishes a general framework for compact, uncertainty-aware spectral imaging that combines minimal optics with advanced deep learning, offering broad utility for real-time biochemical imaging across neuroscience, environmental monitoring, and biomedicine.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows

In the past couple of years, there has been a proliferation in the use of machine learning approaches to represent subgrid-scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical simulations of these flows. Despite its success for different types of flow, the online deployment of a data-driven closure model can cause instabilities and biases in modeling the overall effect of subgrid-scale processes, which in turn leads to inaccurate prediction. To tackle this issue, we exploit the data assimilation technique to correct the physics-based model coupled with the neural network as a surrogate for unresolved flow dynamics in multiscale systems. In particular, we use a set of neural network architectures to learn the correlation between resolved flow variables and the parametrizations of unresolved flow dynamics and formulate a data assimilation approach to correct the hybrid model during their online deployment. We illustrate our framework in a set of applications of the multiscale Lorenz 96 system for which the parametrization model for unresolved scales is exactly known, and the two-dimensional Kraichnan turbulence system for which the parametrization model for unresolved scales is not known a priori. Our analysis, therefore, comprises a predictive dynamical core empowered by (i) a data-driven closure model for subgrid-scale processes, (ii) a data assimilation approach for forecast error correction, and (iii) both data-driven closure and data assimilation procedures. We show significant improvement in the long-term prediction of the underlying chaotic dynamics with our framework compared to using only neural network parametrizations for future prediction. Moreover, we demonstrate that these data-driven parametrization models can handle the non-Gaussian statistics of subgrid-scale processes, and effectively improve the accuracy of outer data assimilation workflow loops in a modular nonintrusive way.

42 ENGINEERING↗
DOE OSTI2019

DeepDriveMD: Deep-Learning Driven Adaptive Molecular Simulations for Protein Folding

Simulations of biological macromolecules are important in understanding the physical basis of complex processes such as protein folding. However, even with increasing computational capacity and specialized architectures, the ability to simulate protein folding at atomistic scales still remains challenging. This stems from the dual aspects of high dimensionality of protein conformational landscapes, and the inability of atomistic molecular dynamics (MD) simulations to sufficiently sample these landscapes to observe folding events. Machine learning/deep learning (ML/DL) techniques, when combined with atomistic MD simulations offer the opportunity to potentially overcome these limitations by: (1) effectively reducing the dimensionality of MD simulations to automatically build latent representations that correspond to biophysically relevant reaction coordinates (RCs), and (2) driving MD simulations to automatically sample potentially novel conformational states based on these RCs. We examine how coupling DL approaches with MD simulations can lead to effective approaches to fold small proteins on supercomputers. In particular, we study the computational costs and effectiveness of scaling DL-coupled MD workflows implemented using RADICAL-Cybertools in folding two prototypical systems, namely Fs-peptide and the fast-folding variant of the villin head piece protein. We demonstrate that a DL-coupled MD workflow is able to effectively learn latent representations and drive adaptive simulations. Compared to traditional MD-based approaches, our approach achieves an effective performance gain in sampling the folded states by at least 2.3x. Together, our study provides quantitative basis to understand how coupling DL approaches to MD simulations, can lead to effective performance gains and reduced times to solution on supercomputing resources.

Lee, Hyungro↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗