Search NASA⌕ Search

SEARCH · Search NASA

Results for “Operator learning”

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

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

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Active operator learning with predictive uncertainty quantification for partial differential equations

With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying reliable surrogate models in scientific applications. Existing uncertainty quantification (UQ) frameworks employ ensembles or Bayesian methods, which can incur substantial computational costs during both training and inference. Here, we propose a lightweight predictive UQ method tailored for Deep operator networks (DeepONets) that also generalizes to other operator networks. Numerical experiments on linear and nonlinear PDEs demonstrate that the framework’s uncertainty estimates are unbiased and provide accurate out-of-distribution uncertainty predictions with a sufficiently large training dataset. Our framework provides fast inference and uncertainty estimates that can efficiently drive outer-loop analyses that would be prohibitively expensive with conventional solvers. We demonstrate how predictive uncertainties can be used in the context of Bayesian optimization and active learning problems to yield improvements in accuracy and data-efficiency for outer-loop optimization procedures. In the active learning setup, we extend the framework to Fourier Neural Operators (FNO) and describe a generalized method for other operator networks. To enable real-time deployment, we introduce an inference strategy based on precomputed trunk outputs and a sparse placement matrix, reducing evaluation time by more than a factor of five. Our method provides a practical route to uncertainty-aware operator learning in time-sensitive settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A variational framework for residual-based adaptivity in neural PDE solvers and operator learning

Residual-based adaptive strategies are widely used in scientific machine learning yet remain largely heuristic. We introduce a variational framework that formalizes these methods through convex transformations of the residual, where different transformations correspond to distinct objective functionals. For instance, exponential weights target uniform error minimization, while linear weights recover quadratic error minimization. This perspective reveals adaptive weighting as a means of selecting sampling distributions that optimize a primal objective, directly linking discretization choices to error metrics. This principled approach yields three key benefits: it enables systematic design of adaptive schemes, reduces discretization error by lowering estimator variance, and enhances learning dynamics by improving gradient signal-to-noise ratio. Extending the framework to operator learning, we demonstrate substantial performance gains across diverse optimizers and architectures. Our results provide a theoretical perspective for residual-based adaptivity and establish a foundation for principled discretization and training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast and accurate reduced-order modeling of a MOOSE-based additive manufacturing model with operator learning

One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on existing simulation tools employed in AM. The goal of the present work is to construct a fast and accurate reduced-order model (ROM) for an AM model developed within the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, ultimately reducing the time/cost of AM control and optimization processes. Our adoption of the operator learning (OL) approach enabled us to learn a family of differential equations produced by altering process variables in the laser’s Gaussian point heat source. More specifically, we used the Fourier neural operator (FNO) and deep operator network (DeepONet) to develop ROMs for time-dependent responses. Furthermore, we benchmarked the performance of these OL methods against a conventional deep neural network (DNN)-based ROM. Ultimately, we found that OL methods offer comparable performance and, in terms of accuracy and generalizability, even outperform DNN at predicting scalar model responses. The DNN-based ROM afforded the fastest training time. Furthermore, all the ROMs were faster than the original MOOSE model yet still provided accurate predictions. FNO had a smaller mean prediction error than DeepONet, with a larger variance for time-dependent responses. Unlike DNN, both FNO and DeepONet were able to simulate time series data without the need for dimensionality reduction techniques. Finally, the present work can help facilitate the AM optimization process by enabling faster execution of simulation tools while still preserving evaluation accuracy.

36 MATERIALS SCIENCE↗
NASA NTRS1984

The Impact of Pictorial Display on Operator Learning and Performance

The effects of pictorially displayed information on human learning and performance of a simple control task were investigated. The controlled system was a harmonic oscillator and the system response was displayed to subjects as either an animated pendulum or a horizontally moving dot. Results indicated that the pendulum display did not effect performance scores but did significantly effect the learning processes of individual operators. The subjects with the pendulum display demonstrated more vertical internal models early in the experiment and the manner in which their internal models were tuned with practice showed increased variability between subjects.

Miller, R. A.↗
DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Adjoint-Operator Learning For A Neural Network

Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.

Barhen, Jacob↗
NASA NTRS2016

Human Flight to Lunar and Beyond - Re-Learning Operations Paradigms

For the first time since the Apollo era, NASA is planning on sending astronauts on flights beyond LEO. The Human Space Flight (HSF) program started with a successful initial flight in Earth orbit, in December 2014. The program will continue with two Exploration Missions (EM): EM-1 will be unmanned and EM-2, carrying astronauts, will follow. NASA established a multi-center team to address the communications, and related tacking/navigation needs. This paper will focus on the lessons learned by the team designing the architecture and operations for the missions. Many of these Beyond Earth Orbit lessons had to be re-learned, as the HSF program has operated for many years in Earth orbit. Unlike the Apollo missions that were largely tracked by a dedicated ground network, the HSF planned missions will be tracked (at distances beyond GEO) by the DSN, a network that mostly serves robotic missions. There have been surprising challenges to the DSN as unique modern human spaceflight needs stretch the experience base beyond that of tracking robotic missions in deep space. Close interaction between the DSN and the HSF community to understand the unique needs (e.g. 2-way voice) resulted in a Concept of Operations (ConOps) that leverages both the deep space robotic and the Human LEO experiences. Several examples will be used to highlight the unique challenges the team faced in establishing the communications and tracking capabilities for HSF missions beyond Earth Orbit, including: Navigation. At LEO, HSF missions can rely on GPS devices for orbit determination. For Lunar-and-beyond HSF missions, techniques such as precision 2-way and 3-way Doppler and ranging, Delta-Difference-of-range, and eventually possibly on-board navigation will be used. At the same time, HSF presents a challenge to navigators, beyond those presented by robotic missions - navigating a dynamic/"noisy" spacecraft. Impact of latency - the delay associated with Round-Trip-Light-Time (RTLT). Imagine trying to have a 2-way discussion (audio or video) with an astronaut, with a 2-3 sec or more delay inserted (for lunar distances) or 20 minutes delay (for Mars distances). Balanced communications link. For robotic missions, there has been a heavy emphasis on higher downlink data rates, e.g. bringing back science data. Higher uplink data rates were of secondary importance, as uplink was used only to send commands (and occasionally small files) to the spacecraft. The ratio of downlink-to-uplink data rates was often 10:1 or more. For HSF, a continuous forward link is established and rates for uplink and downlink are more similar.

Kenny, Edward (Ted)↗
NASA NTRS2016

Human Flight to Lunar and Beyond - Re-Learning Operations Paradigms

For the first time since the Apollo era, NASA is planning on sending astronauts on flights beyond Low-Earth Orbit (LEO). The Human Space Flight (HSF) program started with a successful initial flight in Earth orbit, in December 2014. The program will continue with two Exploration Missions (EM) to Lunar orbit: EM-1 will be unmanned and EM-2, carrying astronauts, will follow. NASA established a multi-center team to address the communications, and related navigation, needs. This paper will focus on the lessons learned in the team, planning for the missions' parts that are beyond Earth orbit. Many of these lessons had to be re-learned, as the HSF program after operated for many years in Earth orbit. Fortunately, the experience base from tracking robotic missions in deep space by the Deep Space Network (DSN) and close interaction with the HSF community to understand the unique needs (e.g. 2-way voice) resulted in a ConOps that leverages of both the deep space robotic and the Human LEO experiences. Several examples will be used to highlight the unique operational needs for HSF missions beyond Earth Orbit, including: - Navigation. At LEO, HSF missions can rely on Global Positioning System (GPS) devices for orbit determination. For Lunar-and-beyond HSF missions, techniques such as precision 2-way and 3-way Doppler and ranging, Delta-Difference-of-range, and eventually on-board navigation will be used. - Impact of latency - the delay associated with Round-Trip-Light-Time (RTLT). Imagine trying to have a 2-way discussion (audio or video) with an astronaut, with a 2-3 sec delay inserted (for Lunar distances) or 20 minutes delay (for Mars distances). - Balanced communications link. For robotic missions, there has been a heavy emphasis on the downlink data rates, bringing back science data from the instruments on-board the spacecraft. Uplink data rates were of secondary importance, used to send commands to the spacecraft. The ratio of downlink-to-uplink data rates was often 10:1 or more. For HSF, rates for uplink and downlink, at least for high-quality video, need to be similar.

Kenny, Ted↗
DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Nonlocal Operator Learning with Uncertainty Quantification

The goal of this work is to develop a Bayesian framework to characterize the uncertainty of material response when using a nonlocal, homogenized model to describe wave propagation through heterogeneous, disordered materials. Our approach is based on an operator regression technique combined with Bayesian optimization, through which the nonlocal kernel for a specific disordered microstructure is investigated.

36 MATERIALS SCIENCE↗