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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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NASA NTRSDate not supplied

Imbalanced Multi-layer Cloud Classification with Advanced Baseline Imager (ABI) and CloudSat/CALIPSO Data

Clouds at different altitudes play different roles in Earth’s climate. Comprehensive understanding of overlapping clouds is important for climate and weather prediction. The East Pacific region is where El Ni˜no and La Ni˜na originate and where multi-layer clouds frequently occur. The overlap of clouds at different altitudes in this region increases the classification complexity for cloud-based climatological studies. Unlike prior work in cloud layer classification that assumes single layer or two-layer of clouds, in this work, we consider multi-layer cloud classification with 8 cloud-level classes (clear-sky, high, middle, low, high+middle, high+low, middle+low, high+middle+low). We develop and analyze machine learning models on features extracted from satellite images from the East Pacific regions collected by GOES Advanced Baseline Imager (ABI). These are used to classify CloudSat/CALIPSO observed multi-layer clouds. Due to the imbalanced nature of the data, we investigate the adoption of conventional resampling methods, as well as deep learning methods with data augmentation. In our experiments, we utilize the random forest classifier and Multilayer perceptron classifier with data augmentation methods to reduce the class imbalance during training. With these approaches, we achieve a classification accuracy of 83.6% without exploiting any ancillary information.

machine learning↗
NASA NTRS2023

Predicting Two-Dimensional Airfoil Performance Using Graph Neural Networks

Computer simulations require the use of meshes to simulate geometries. These meshes capture important geometric features of the design and can be used in machine learning modeling. This report explores the use of graph neural networks (GNNs) to learn features from two-dimensional (2D) airfoil designs represented as a set of nodes connected using edges. This type of network is common in aerospace applications: most geometries are represented as a mesh in order to perform analysis. The objective of this work is to use GNNs to predict the performance of 2D airfoils generated using the program XFOIL. The predicted performance parameters include bulk quantities such as coefficients of lift (C L ), drag (C d , C dp ), moment (C m ), and node-specific quantities such as coefficient of pressure (C p ). In this report, a spline convolutional graph-based neural network is compared with deep learning neural networks to predict both bulk and node-specific quantities. The findings indicate the GNNs are able to predict bulk quantities quite well; however, when the number of outputs is increased, the deep neural network (DNN) proves to be better in its prediction capability. Two different normalization strategies were compared in the training of both GNNs and DNNs: minmax and standard deviation. In both types of networks, standard deviation scaling proved to be the best.

machine learning↗
NASA NTRSDate not supplied

A Quantitative Analysis On the Use Of Supervised Machine Learning in Earth Science

Several recent papers have investigated different challenges in applying machine learning (ML) techniques to Earth science problems. The challenges listed range from interpretability of the results to computational demand to data issues. In this paper, we focus on specific challenges listed in the review papers that are centered around training data, as the size of training data is important in applying deep learning (DL) techniques. We are in the process of conducting a literature survey to better understand these challenges as well as to understand any trends. As part of this survey, our review has encompassed Earth science papers from AGU, AMS, IEEE and SPIE journals covering the last ten years and focused on papers that utilize supervised ML techniques.

Katrina S Virts↗
DOE OSTI2025

Operator learning for energy-efficient building ventilation control with computational fluid dynamics simulation of a real-world classroom

Energy-efficient ventilation control plays an important role in reducing building energy consumption while ensuring occupant health and comfort. While Computational Fluid Dynamics (CFD) simulations provide detailed and physically accurate representations of indoor airflow, their high computational cost limits their use in real-time building control. In this work, we present a neural operator learning framework that combines the physical accuracy of CFD with the computational efficiency of machine learning to enable building ventilation control with the high-fidelity fluid dynamics models. Our method jointly optimizes the airflow supply rates and vent angles to reduce energy use and adhere to air quality constraints. We train an ensemble of neural operator transformer models to learn the mapping from building control actions to airflow fields using high-resolution CFD data. This learned neural operator is then embedded in an optimization-based control framework for building ventilation control. Experimental results show that our approach achieves significant energy savings compared to maximum airflow rate control, rule-based control, as well as data-driven control methods using spatially averaged CO 2 prediction and deep learning–based reduced-order models, while consistently maintaining safe indoor air quality. These results highlight the practicality and scalability of our method in maintaining energy efficiency and indoor air quality in real-world buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2024

Celebrating 10 Years of the Sub-Seasonal to Seasonal Prediction Project and Looking to the Future

The conference clearly demonstrated the increasing interest and growth of the scientific community working on the development and application of sub-seasonal to seasonal prediction since the start of the World Weather Research Programme (WWRP)/World Climate Research Programme (WCRP) sub-seasonal to seasonal (S2S) prediction project in 2013. The conference, which was held at the University of Reading (United Kingdom), was organized into three main themes as briefly summarized below, with eleven invited talks, 74 oral contributed talks, and 101 posters. The conference also included a two-hour breakout session, wherein eight groups discussed the current state and prospect for S2S prediction, and an early career researcher event. A summary of these discussions and recommendations is presented below. The conference web page (https://research.reading.ac.uk/s2s-summit2023/) is archived at the University of Reading. Introductory comments by representatives of the World Meteorological Organization (WMO) WWRP and WCRP emphasized the importance of the weather–climate linkage, targeted by S2S forecasts (from 2 weeks to a season ahead), addressing the challenges of creating “end-to-end” forecasts that encompass the entire climate-services chain from the prediction science and forecast, to the development and issuing of forecast products tailored to informing user-decisions. They also emphasized the efficacy of multi-model ensemble efforts and databases to foster collaborations internationally and between operational centres and academia. Although the WWRP/WCRP S2S project comes to an end in 2023, S2S prediction will remain an important focus for WWRP and WCRP. In WWRP, a new project called SAGE (Sub-seasonal to seasonal predictions for Agriculture and Environment) will start in 2024. Another important legacy of the S2S project will be the maintenance of the S2S database (Vitart et al. 2017) and the establishment of a WMO Lead Center for sub-seasonal prediction multi-model ensemble (LC-SSPMME) which will provide real-time multi-model S2S climate information. In two keynote presentations, Prof. Brian Hoskins (University of Reading) and Dr. Gilbert Brunet (Australian Bureau of Meteorology) discussed the potential of S2S predictability and the ongoing journey for understanding and improving these predictions. This conference was a sequel to the International Conference on Sub-seasonal to Seasonal Prediction (Robertson et al., 2014) which took place in College Park (Maryland, USA) in February 2014 to celebrate the start of the WWRP/WCRP S2S project, and to WCRP and WWRP conferences in Boulder, USA, in 2018 (Merryfield et al., 2020). A significant development compared to the previous S2S conferences was the large number of presentations on research to operation (R2O) and S2S applications and on the use of artificial intelligence and machine learning (AI/ML) methods for S2S prediction. Some of these methods provide empirical S2S forecasts which are competitive with state-of-the-art dynamical models. Other presentations demonstrated that AI/ML can provide alternative calibration of dynamical model outputs to traditional methods. Several talks and posters highlighted the increasing use of AI/ML, including deep learning, in S2S forecast post-processing and using AI to identify higher flow-dependent skill. Finally, some presentations demonstrated the value of AI/ML methods for a better understanding of S2S sources of predictability and attribution of extreme events.

S. J. Woolnough↗
DOE OSTI2025

Advancing stream temperature prediction with a generalizable large-sample framework across CONUS river reaches

Accurately predicting stream temperature in ungauged basins remains a critical challenge for water resource management, thermoelectric power plant cooling, and ecosystem conservation. Large-sample machine learning models trained on hundreds of well-monitored river basins have shown remarkable performance; however, such models have yet to be developed solely using forcing data that can be readily extracted to simulate stream temperatures anywhere in the contiguous United States (CONUS). In this study, we present a scalable, large-sample deep learning framework using Long Short-Term Memory (LSTM) networks to simulate daily stream temperatures in ungauged basins across the CONUS. The framework leverages both modeled reanalysis of meteorological and streamflow inputs as well as static attributes available for all 2.7 million CONUS river reaches in the National Hydrography Dataset Plus (NHDPlusV2). By generating dynamical inputs from predefined thermally relevant upstream contributing areas, rather than the entire upstream basin, the model also offers improvements in very large basins where full-basin averaging can dilute the most important influences on stream temperature. Evaluated across 300 basins, the model achieves a median Mean Absolute Error (MAE) of 1.1 °C and a Nash-Sutcliffe Efficiency (NSE) of 0.95 on temporally and spatially distinct test folds—comparable to models trained exclusively using meteorological and streamflow observational data. The flexible, high-performing framework generalizes to any unmonitored river reach without significant regulation or unnatural thermal input immediately upstream, substantially expanding predictive capabilities in data-scarce regions.

Hydrology↗
NASA NTRSDate not supplied

Deep Neural Network Based Convergence Classification for Computational Fluid Dynamics

A supervised deep learning approach is coupled with heuristic convergence criteria to construct a classification model for detecting the completion (convergence) of computational fluid dynamics (CFD) simulations. Heuristic convergence criteria alone are not always sufficient and more complex decisions are often left to a human analyst. The proposed approach leverages heuristic convergence criteria as well as two deep neural network (DNN) models, one binary and one multi-class, to improve the efficiency and consistency of convergence classification across a wide range of flight regimes. The DNN models presented are each trained on a subset of ascent aerodynamic CFD simulations for NASA’s Space Launch System and were produced using NASA’s unstructured Navier-Stokes solver FUN3D. Individual solutions are analyzed intermittently and are classified as sufficiently converged, further iterations required, or switch from steady Reynolds Averaged Navier-Stokes (RANS) to unsteady RANS CFD based on the iterative histories of four aerodynamic coefficients. The implemented classification model is shown to produce solutions that closely correlate to solutions produced by a human analyst. This work lays groundwork for expanding the capabilities of DNNs for automating and improving more of the CFD process.

SLS↗
DOE OSTI2026

Machine learning approach for vibronically renormalized electronic band structures

Here, we present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the nonperturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming ab initio calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT). We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

ELM2.1-XGBfire1.0: improving wildfire prediction by integrating a machine learning fire model in a land surface model

Wildfires have shown increasing trends in both frequency and severity across the contiguous United States (CONUS). However, process-based fire models have difficulties in accurately simulating the burned area over the CONUS due to a simplification of the physical process and cannot capture the interplay among fire, ignition, climate, and human activities. The deficiency of burned area simulation deteriorates the description of fire impact on energy balance, water budget, and carbon fluxes in the Earth system models (ESMs). Alternatively, fire models based on machine learning (ML), which capture statistical relationships between the burned area and environmental factors, have shown promising burned area predictions and corresponding fire impact simulation. We develop a hybrid framework (ELM2.1-XGBFire1.0) that integrates an eXtreme Gradient Boosting (XGBoost) wildfire model with the Energy Exascale Earth System Model (E3SM) land model (ELM) version 2.1. A Fortran–C–Python deep learning bridge is adapted to support online communication between ELM and the ML fire model. Specifically, the burned area predicted by the ML-based wildfire model is directly passed to ELM to adjust the carbon pool and vegetation dynamics after disturbance, which are then used as predictors in the ML-based fire model in the next time step. Evaluated against the historical burned area from Global Fire Emissions Database 5 from 2001–2019, the ELM2.1-XGBFire1.0 outperforms process-based fire models in terms of spatial distribution and seasonal variations. The ELM2.1-XGBFire1.0 has proven to be a new tool for studying vegetation–fire interactions and, more importantly, enables seamless exploration of climate–fire feedback, working as an active component of E3SM.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Synthetic Atmospheric River Ensembles Generated by Deep-AR

This dataset contains 35,850 synthetic landfalling atmospheric river (AR) realizations generated by the Deep-AR two-stage deep-learning framework over the Northeast Pacific and U.S. West Coast. The archive contains 25 stochastic ensemble members for each of 1,434 held-out observed seed events. Each synthetic realization is initialized from conditions 48 hours before the corresponding observed AR landfall and is generated autoregressively at 6-hour intervals over a 144-hour period. Deep-AR combines a deterministic residual network (ResNet) that advances the large-scale atmospheric state with a Wasserstein generative adversarial network (WGAN) that produces stochastic, high-resolution fields. Each HDF5 file contains 0.25° gridded synthetic integrated vapor transport components (qu, qv), 10 m wind components (u10, v10), and 6-hour accumulated precipitation on a common 200 × 480 grid. The files also include coordinate and datetime arrays. This dataset supports AR hazard analysis, ensemble-based uncertainty characterization, precipitation-extremes research, and regional stress testing. Synthetic files follow the naming convention deepar.model.YYYYMMDD.HHMMSS.vNN.h5. YYYYMMDD.HHMMSS identifies the UTC initial-condition timestamp, which occurs 48 hours before the diagnosed observed landfall, and vNN identifies the zero-padded ensemble member, ranging from v01 through v25. Each synthetic file can be paired with its corresponding observed file by matching the initial-condition timestamp. The paired observed file follows the naming convention deepar.obs.YYYYMMDD.HHMMSS.h5 and is available in the separately registered oracle/deepar.obs dataset at https://wdh.energy.gov/ds/oracle/deepar.obs (DOI: https://doi.org/10.21947/3377671).

17 WIND ENERGY↗
DOE OSTI2025

Accelerating charge estimation in molecular dynamics simulations using physics-informed neural networks: corrosion applications

Molecular Dynamics (MD) simulations are used to understand the effects of corrosion on metallic materials in salt brine. Reactive force fields in classical MD enable accurate modeling of bond formation and breakage in the aqueous medium and at the metal-electrolyte interface, while also facilitating dynamic partial charge equilibration. However, MD simulations are computationally intensive and unsuitable for modeling the long time scales characteristic of corrosive phenomena. To address this, we develop reduced-order machine learning models that provide accurate and efficient predictions of charge density in corrosive environments. Specifically, we use Long Short-Term Memory (LSTM) networks to forecast charge density evolution based on atomic environments represented by Smooth Overlap of Atomic Positions (SOAP) descriptors. A physics-informed loss function enforces charge neutrality and electronegativity equivalence. The atomic charges predicted by the deep learning model trained on this work were obtained two orders of magnitude faster than those from molecular dynamics (MD) simulations, with an error of less than 3% compared to the MD-obtained charges, even in extrapolative scenarios, while adhering to physical constraints. This demonstrates the excellent accuracy, computational efficiency, and validity of the developed model. Lastly, even though developed for corrosion, these protocols are formulated in a phenomenon-agnostic manner, allowing application to various variable-charge interatomic potentials and related fields.

Atomistic models↗
DOE OSTI2025

Self-supervised physics-informed generative networks for phase retrieval from a single X-ray hologram

X-ray phase contrast imaging significantly improves the visualization of structures with weak or uniform absorption, broadening its applications across a wide range of scientific disciplines. Propagation-based phase contrast is particularly suitable for time- or dose-critical in vivo/in situ/operando (tomography) experiments because it requires only a single intensity measurement. However, the phase information of the wave field is lost during the measurement and must be recovered. Conventional algebraic and iterative methods often rely on specific approximations or boundary conditions that may not be met by many samples or experimental setups. In addition, they require manual tuning of reconstruction parameters by experts, making them less adaptable for complex or variable conditions. Here we present a self-learning approach for solving the inverse problem of phase retrieval in the near-field regime of Fresnel theory using a single intensity measurement (hologram). A physics-informed generative adversarial network is employed to reconstruct both the phase and absorbance of the unpropagated wave field in the sample plane from a single hologram. Unlike most state-of-the-art deep learning approaches for phase retrieval, our approach does not require paired, unpaired, or simulated training data. This significantly broadens the applicability of our approach, as acquiring or generating suitable training data remains a major challenge due to the wide variability in sample types and experimental configurations. The algorithm demonstrates robust and consistent performance across diverse imaging conditions and sample types, delivering quantitative, high-quality reconstructions for both simulated data and experimental datasets acquired at beamline P05 at PETRA III (DESY, Hamburg), operated by Helmholtz-Zentrum Hereon. Furthermore, it enables the simultaneous retrieval of both phase and absorption information.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Simulated wildfire burned area over the CONUS during 2001-2020

Wildfires have shown increasing trends in both frequency and severity across the Contiguous United States (CONUS). However, process-based fire models have difficulties in accurately simulating the burned area over the CONUS due to a simplification of the physical process and cannot capture the interplay among fire, ignition, climate, and human activities. The deficiency of burned area simulation deteriorates the description of fire impact on energy balance, water budget, and carbon fluxes in the Earth System Models (ESMs). Alternatively, machine learning (ML) based fire models, which capture statistical relationships between the burned area and environmental factors, have shown promising burned area predictions and corresponding fire impact simulation. We develop a hybrid framework (ML4Fire-XGB) that integrates a pretrained eXtreme Gradient Boosting (XGBoost) wildfire model with the Energy Exascale Earth System Model (E3SM) land model (ELM). A Fortran-C-Python deep learning bridge is adapted to support online communication between ELM and the ML fire model. Specifically, the burned area predicted by the ML-based wildfire model is directly passed to ELM to adjust the carbon pool and vegetation dynamics after disturbance, which are then used as predictors in the ML-based fire model in the next time step. Evaluated against the historical burned area from Global Fire Emissions Database 5 from 2001-2020, the ML4Fire-XGB model outperforms process-based fire models in terms of spatial distribution and seasonal variations. Sensitivity analysis confirms that the ML4Fire-XGB well captures the responses of the burned area to rising temperatures. The ML4Fire-XGB model has proved to be a new tool for studying vegetation-fire interactions, and more importantly, enables seamless exploration of climate-fire feedback, working as an active component in E3SM.

Liu, Ye↗
DOE OSTI2024

Real-time tracking of structural evolution in 2D MXenes using theory-enhanced machine learning

In situ Electron Energy Loss Spectroscopy (EELS) combined with Transmission Electron Microscopy (TEM) has traditionally been pivotal for understanding how material processing choices affect local structure and composition. However, the ability to monitor and respond to ultrafast transient changes, now achievable with EELS and TEM, necessitates innovative analytical frameworks. Here, we introduce a machine learning (ML) framework tailored for the real-time assessment and characterization of in operando EELS Spectrum Images (EELS-SI). We focus on 2D MXenes as the sample material system, specifically targeting the understanding and control of their atomic-scale structural transformations that critically influence their electronic and optical properties. This approach requires fewer labeled training data points than typical deep learning classification methods. By integrating computationally generated structures of MXenes and experimental datasets into a unified latent space using Variational Autoencoders (VAE) in a unique training method, our framework accurately predicts structural evolutions at latencies pertinent to closed-loop processing within the TEM. This study presents a critical advancement in enabling automated, on-the-fly synthesis and characterization, significantly enhancing capabilities for materials discovery and the precision engineering of functional materials at the atomic scale.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Simulation-based inference for parameter estimation of complex watershed simulators

High-resolution, spatially distributed process-based (PB) simulators are widely employed in the study of complex catchment processes and their responses to a changing climate. However, calibrating these PB simulators using observed data remains a significant challenge due to several persistent issues, including the following: (1) intractability stemming from the computational demands and complex responses of simulators, which renders infeasible calculation of the conditional probability of parameters and data, and (2) uncertainty stemming from the choice of simplified representations of complex natural hydrologic processes. Here, we demonstrate how simulation-based inference (SBI) can help address both of these challenges with respect to parameter estimation. SBI uses a learned mapping between the parameter space and observed data to estimate parameters for the generation of calibrated simulations. To demonstrate the potential of SBI in hydrologic modeling, we conduct a set of synthetic experiments to infer two common physical parameters – Manning's coefficient and hydraulic conductivity – using a representation of a snowmelt-dominated catchment in Colorado, USA. We introduce novel deep-learning (DL) components to the SBI approach, including an “emulator” as a surrogate for the PB simulator to rapidly explore parameter responses. We also employ a density-based neural network to represent the joint probability of parameters and data without strong assumptions about its functional form. While addressing intractability, we also show that, if the simulator does not represent the system under study well enough, SBI can yield unreliable parameter estimates. Approaches to adopting the SBI framework for cases in which multiple simulator(s) may be adequate are introduced using a performance-weighting approach. The synthetic experiments presented here test the performance of SBI, using the relationship between the surrogate and PB simulators as a proxy for the real case.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Reduced‐Order Modeling for Linearized Representations of Microphysical Process Rates

Abstract Representing cloud microphysical processes in large scale atmospheric models is challenging because many processes depend on the details of the droplet size distribution (DSD, the spectrum of droplets with different sizes in a cloud). While full or partial statistical moments of droplet size distributions are the typical variables used in bulk models, prognostic moments are limited in their ability to represent microphysical processes across the range of conditions experienced in the atmosphere. Microphysical parameterizations employing prognostic moments are known to suffer from structural uncertainty in their representations of inherently higher dimensional cloud processes, which limit model fidelity and lead to forecasting errors. Here we investigate how data‐driven reduced‐order modeling can be used to learn predictors for microphysical process rates in bulk microphysics schemes in an unsupervised manner from higher dimensional bin distributions. Using simulations characteristic of marine stratiform clouds, we simultaneously learn lower dimensional representations of droplet size distributions and predict the evolution of the microphysical state of the system. Droplet collision‐coalescence, the main process for generating warm rain, is estimated to have an intrinsic dimension of three. This intrinsic dimension provides a lower limit on the number of degrees of freedom needed to accurately represent collision‐coalescence in models. We demonstrate how deep learning based reduced‐order modeling can be used to discover intrinsic coordinates describing the microphysical state of the system, where process rates such as collision‐coalescence are globally linearized. These implicitly learned representations of the DSD retain more information about the DSD than typical moment‐based representations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Improving North American Wildfire Prediction by Integrating a Machine-Learning Fire Model in a Land Surface Model

Wildfires have shown increasing trends in both frequency and severity across the Contiguous United States (CONUS). However, process-based fire models have difficulties in accurately simulating the burned area over the CONUS due to a simplification of the physical process and cannot capture the interplay among fire, ignition, climate, and human activities. The deficiency of burned area simulation deteriorates the description of fire impact on energy balance, water budget, and carbon fluxes in the Earth System Models (ESMs). Alternatively, machine learning (ML) based fire models, which capture statistical relationships between the burned area and environmental factors, have shown promising burned area predictions and corresponding fire impact simulation. We develop a hybrid framework (ML4Fire-XGB) that integrates a pretrained eXtreme Gradient Boosting (XGBoost) wildfire model with the Energy Exascale Earth System Model (E3SM) land model (ELM) version 2.1. A Fortran-C-Python deep learning bridge is adapted to support online communication between ELM and the ML fire model. Specifically, the burned area predicted by the ML-based wildfire model is directly passed to ELM to adjust the carbon pool and vegetation dynamics after disturbance, which are then used as predictors in the ML-based fire model in the next time step. Evaluated against the historical burned area from Global Fire Emissions Database 5 from 2001-2020, the ML4Fire-XGB model outperforms process-based fire models in terms of spatial distribution and seasonal variations. Sensitivity analysis confirms that the ML4Fire-XGB well captures the responses of the burned area to rising temperatures. The ML4Fire-XGB model has proved to be a new tool for studying vegetation-fire interactions, and more importantly, enables seamless exploration of climate-fire feedback, working as an active component in E3SM.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks

Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still be challenging, often resulting in unsatisfactory accuracy and efficiency. In this work, we demonstrate that the failure of plain physics-informed neural networks arises from the significant discrepancy in the convergence rate of residuals at different training points, where the slowest convergence rate dominates the overall solution convergence. Based on these observations, we propose a pointwise adaptive weighting method that balances the residual decay rate across different training points. The performance of our proposed adaptive weighting method is compared with current state-of-the-art adaptive weighting methods on benchmark problems for both physics-informed neural networks and physics-informed deep operator networks. In conclusion, through extensive numerical results we demonstrate that our proposed approach of balanced residual decay rates offers several advantages, including bounded weights, high prediction accuracy, fast convergence rate, low training uncertainty, low computational cost, and ease of hyperparameter tuning.

Balanced convergence rate↗