Search NASA⌕ Search

SEARCH · Search NASA

Results for “Multifidelity 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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Comparison of multifidelity machine learning models for potential energy surfaces

Multifidelity modeling is a technique for fusing the information from two or more datasets into one model. It is particularly advantageous when one dataset contains few accurate results and the other contains many less accurate results. Within the context of modeling potential energy surfaces, the low-fidelity dataset can be made up of a large number of inexpensive energy computations that provide adequate coverage of the N-dimensional space spanned by the molecular internal coordinates. The high-fidelity dataset can provide fewer but more accurate electronic energies for the molecule in question. Here, we compare the performance of several neural network-based approaches to multifidelity modeling. We show that the four methods (dual, Δ-learning, weight transfer, and Meng–Karniadakis neural networks) outperform a traditional implementation of a neural network, given the same amount of training data. We also show that the Δ-learning approach is the most practical and tends to provide the most accurate model.

Chemistry↗
DOE OSTI2023

Multifidelity Active Learning for Failure Estimation of TRISO Nuclear Fuel

The Tristructural isotropic (TRISO)-coated particle fuel is a robust nuclear fuel proposed to be used for multiple modern nuclear technologies. Therefore, characterizing its safety is vital for the reliable operation of nuclear technologies. However, the TRISO fuel failure probabilities are small and the computational model is time consuming to evaluate them using traditional Monte Carlo-type approaches. In the paper, we present a multifidelity active learning approach to efficiently estimate small failure probabilities given an expensive computational model. Active learning suggests the next best training set for optimal subsequent predictive performance and multifidelity modeling uses cheaper low-fidelity models to approximate the high-fidelity model output. After presenting the multifidelity active learning approach, we apply it to efficiently predict TRISO failure probability and make comparisons to the reference results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Adaptive, Active Learning, and Multifidelity Monte Carlo Methods in the MOOSE Stochastic Tools Module

MOOSE is an open-source computational platform for constructing multi-physics models and executing them in a massively parallel fashion. It has a stochastic tools module (STM) for forward/inverse uncertainty quantification (UQ) and surrogate modeling. This presentation details some recent developments to the STM with respect to the implementation of adaptive, active learning, and multifidelity Monte Carlo methods for forward UQ of computational models. Specifically, the adaptive Monte Carlo methods include Markov Chain Monte Carlo (MCMC)-driven algorithms like adaptive importance sampling and parallelized subset simulation for statistical QoI estimation, rare events analysis, and stochastic gradient-free optimization. The active learning methods include Gaussian Process (GP) surrogates and their training via Adam optimization, design of acquisition functions, and integration with samplers like Monte Carlo, adaptive importance, and parallelized subset simulation. These active learning methods are also designed to work in a batch mode, wherein, the required calls to the full computational model are executed in parallel whenever a user-specified batch size is met. The multifidelity methods in STM are broadly divided into two categories: hierarchical, where a defined hierarchy exists among the low-fidelity models, and peer, where all the low-fidelity models are treated equally. A GP surrogate is used to learn the differences between the low- and high-fidelity models in both multifidelity categories, and acquisition functions from the active learning classes are used to decide whether to rely on a low-fidelity model or call the expensive high-fidelity model. Alongside the software description and usage, applications are also presented to nuclear engineering computational models including a TRISO nuclear fuel particle, a reactor pressure vessel, and a heat-pipe microreactor.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Bayesian, Multifidelity Operator Learning for Complex Engineering Systems–A Position Paper

Abstract Deep learning has significantly improved the state-of-the-art in computer vision and natural language processing, and holds great potential to design effective tools for predicting and simulating complex engineering systems. In particular, scientific machine learning seeks to apply the power of deep learning to scientific and engineering tasks, with operator learning (OL) emerging as a particularly effective tool. OL can approximate nonlinear operators arising in complex engineering systems, making it useful for simulating, designing, and controlling those systems. In this position paper, we provide a comprehensive overview of OL, including its potential applications to complex engineering domains. We cover three variations of OL approaches: deterministic OL for modeling nonautonomous systems, OL with uncertainty quantification (UQ) capabilities, and multifidelity OL. For each variation, we discuss drawbacks and potential applications to engineering, in addition to providing a detailed explanation. We also highlight how multifidelity OL approaches with UQ capabilities can be used to design, optimize, and control engineering systems. Finally, we outline some potential challenges for OL within the engineering domain.

Computer Science↗
DOE OSTI2023

Reliable extrapolation of deep neural operators informed by physics or sparse observations

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity, via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias–variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information—the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Furthermore, our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed.

42 ENGINEERING↗
DOE OSTI2024

Quasi-Classical Trajectory Calculation of Rate Constants Using an Ab Initio Trained Machine Learning Model (aML-MD) with Multifidelity Data

Machine learning (ML) provides a great opportunity for the construction of models with improved accuracy in classical molecular dynamics (MD). However, the accuracy of a ML trained model is limited by the quality and quantity of the training data. Generating large sets of accurate ab initio training data can require significant computational resources. Furthermore, inconsistent or incompatible data with different accuracies obtained using different methods may lead to biased or unreliable ML models that do not accurately represent the underlying physics. Recently, transfer learning showed its potential for avoiding these problems as well as for improving the accuracy, efficiency, and generalization of ML models using multifidelity data. In this work, ab initio trained ML-based MD (aML-MD) models are developed through transfer learning using DFT and multireference data from multiple sources with varying accuracy within the Deep Potential MD framework. Further, the accuracy of the force field is demonstrated by calculating rate constants for the H + HO 2 → H 2 + 3 O 2 reaction using quasi-classical trajectories. We show that the aML-MD model with transfer learning can accurately predict the rate constants while reducing the computational cost by more than five times compared to the use of more expensive quantum chemistry training data sets. Hence, the aML-MD model with transfer learning shows great potential in using multifidelity data to reduce the computational cost involved in generating the training set for these potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Transfer learning of neural surrogates on multifidelity groundwater simulations

Multifidelity data used in the paper published in Advances in Water Resources 206 (2025) 105140, https://doi.org/10.1016/j.advwatres.2025.105140 The code used to process the data is openly available on GitHub at https://github.com/Model-Reduction-and-UQ-Group/Transfer_Learning_K_reconstruction Computationally inexpensive surrogates of process-based models, such as deep neural networks, enable ensemble-based computations used in risk assessment, data assimilation, etc. However, generation of large datasets required to train a neural network can be as expensive as the ensemble simulations themselves. We ameliorate this challenge by using data from multifidelity (MF) groundwater simulations and transfer learning (TL) to reduce data generation costs while maintaining model accuracy. As a computational example, we train a deep convolutional neural network (CNN) to reconstruct permeability fields from saturation maps derived from a multiphase flow model. Starting with very low- and low-fidelity data generated on increasingly coarse meshes, we pretrain the CNN, followed by output-layer training and fine-tuning using only a limited number of high-fidelity samples. We demonstrate the surrogate’s robustness when interpreting low-quality inputs—such as interpolated maps or data affected by noise—which has strong implications for the applicability in practical hydrogeological scenarios. This multilevel MF-TL strategy achieves a favorable trade-off between computational efficiency and predictive accuracy, significantly outperforming high-fidelity-only approaches under the same computational budget.

Chiofalo, Alessia [University of Bologna] (ORCID:0↗
DOE OSTI2023

A Multifidelity and Multimodal Machine Learning Approach for Extracting Bonding Environments of Impurities and Dopants from X-ray Spectroscopies

Extended X-ray absorption fine structure (EXAFS) spectroscopy is crucial for determining the coordination environment of impurities and dopants; however, it requires difficult measurements. X-ray absorption near edge structure (XANES) spectroscopy and X-ray emission spectroscopy (XES) can be obtained easily but cannot be converted to determine structures. In this work we develop tools to map measured XANES to the EXAFS signal through machine learning, thereby facilitating the use of EXAFS structural-determination analyses on XANES data. Through the use of Deep Operator Networks (DeepONets), we are able to accurately predict the EXAFS spectrum between 6 and 14 Å -1 from the first 6 Å -1 (~100 eV) of the absorption spectrum of Cu 2+ substitutional defects in the Fe 3+ mineral hematite (a-Fe 2 O 3 ). This surprising finding implies that theoretical analyses of X-ray absorption spectra could be implemented that extract the same conclusions as high-quality EXAFS studies from spectra collected over a much smaller range of photon energies. To encourage similar efforts, the simulated x-ray spectra, machine learning, and fitting code is made publicly available.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

A multifidelity deep operator network approach to closure for multiscale systems

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies, even instabilities, due to the improper accounting of the interaction between the resolved and unresolved scales of the multiscale system (known as the closure problem). In the current work, we interpret closure as a multifidelity problem and use a multifidelity deep operator network (DeepONet) framework to address it. In addition, to enhance the stability and/or accuracy of the multifidelity-based closure, we employ the recently developed ``in-the-loop" training approach from the literature on coupling physics and machine learning models. The resulting approach is tested on shock advection for the one-dimensional viscous Burgers equation and vortex merging for the two-dimensional Navier-Stokes equations. Furthermore, the numerical experiments show significant improvement of the predictive ability of the closure-corrected PROM over the un-corrected one both in the interpolative and the extrapolative regimes.

42 ENGINEERING↗
DOE OSTI2025

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

Autoencoders↗
DOE OSTI2023

Efficient Reliability Analysis using Generalized Multifidelity Modeling and Explainable Active Learning

To assess the reliability of critical technologies like nuclear plants and infrastructure systems and improve the robustness of design, engineers have to quantify the uncertainties surrounding the system behavior accurately. However, the complexity of the problem can make standard reliability analysis algorithms prohibitively expensive, primarily due to the high computational cost of estimating the system response at each iteration. This cost can be greatly reduced by using multi-fidelity modeling and machine learning to build a surrogate model to replace the expensive response function. We propose a general and robust method for building surrogates from multiple Low Fidelity (LF) models coupled with machine learning to retain accuracy. Our framework first constructs “Corrected Low Fidelity models” (CLFs) by coupling a High Fidelity (HF) model inferred Gaussian Process correction term with each of the LF models. It then uses the correction terms to assign model probabilities to each of these CLFs in an explainable way before using them to assemble the final surrogate. No assumptions are made about the type of the LF models or their correlation with the HF model. The proposed surrogate modeling framework is used within the subset simulation algorithm (a variance-reduced MCMC-based reliability analysis algorithm) for enhanced efficiency. Additionally, an active learning step is added to the algorithm to adaptively decide when the surrogate is not sufficiently accurate, at which point the HF model is called and used to refine the surrogate. Through a frame buckling example, our method is shown to be highly efficient at reducing the expensive HF model calls while accurately estimating the failure probability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

General Multifidelity Surrogate Models: Framework and Active-Learning Strategies for Efficient Rare Event Simulation

Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process more feasible, but merging information from multiple low-fidelity and high-fidelity models poses several challenges. Here, this paper presents a robust multi-fidelity surrogate modeling strategy in which the multi-fidelity surrogate is assembled using an active learning strategy using an on-the-fly model adequacy assessment set within a subset simulation framework for efficient reliability analysis. The multi-fidelity surrogate is assembled by first applying a Gaussian process correction to each low-fidelity model and assigning a model probability based on the model's local predictive accuracy and cost. Three strategies are proposed to fuse these individual surrogates into an overall surrogate model based on model averaging and deterministic/stochastic model selection. The strategies also dictate which model evaluations are necessary. No assumptions are made about the relationships between low-fidelity models, while the high-fidelity model is assumed to be the most accurate and most computationally expensive model. Through two analytical and two numerical case studies, including a case study evaluating the failure probability of Tristructural isotropic-coated (TRISO) nuclear fuels, the algorithm is shown to be highly accurate while drastically reducing the number of high-fidelity model calls (and hence computational cost).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Stacked networks improve physics-informed training: Applications to neural networks and deep operator networks

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can happen to be difficult or impossible to train accurately. Here, we present a novel multifidelity framework for stacking physics-informed neural networks and operator networks that facilitates training. We successively build a chain of networks, where the output at one step can act as a low-fidelity input for training a longer chain, gradually increasing the expressivity of the learnt model. The equations imposed at each step of the iterative process can be the same or different (akin to simulated annealing). The iterative (stacking) nature of the proposed method allows us to learn progressively features of a solution which could have been hard to learn directly. Through benchmark problems including a nonlinear pendulum, the wave equation, and the viscous Burgers equation, we show how stacking can be used to improve the accuracy and reduce the required size of physics-informed neural networks and operator networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Multifidelity deep operator networks for data-driven and physics-informed problems

Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either from experiments or simulations. In this work, we present a composite Deep Operator Network (DeepONet) for learning using two datasets with different levels of fidelity to accurately learn complex operators when sufficient high-fidelity data is not available. Additionally, we demonstrate that the presence of low-fidelity data can improve the predictions of physics-informed learning with DeepONets. We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland, using two different fidelity models and also using the same physical model at two different resolutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Projection-based multifidelity linear regression for data-scarce applications

Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear regression targeting data-limited applications with high-dimensional outputs. Multifidelity methods integrate many inexpensive low-fidelity model evaluations with limited, costly high-fidelity evaluations. We introduce two projection-based multifidelity linear regression approaches with linear and nonlinear features that leverage principal component basis vectors for dimensionality reduction and combine multifidelity data through: (i) a direct data augmentation using low-fidelity data, and (ii) a data augmentation incorporating explicit linear corrections between low-fidelity and high-fidelity data. The data augmentation approaches combine high-fidelity and low-fidelity data into a unified training set and train the linear regression model through weighted least squares with fidelity-specific weights. We introduce a proximity-based weighting scheme with automatic weight selection strategy through cross-validation. Here, the proposed multifidelity linear regression methods are demonstrated on approximating the surface pressure field of a hypersonic vehicle in flight and the temperature field on an aircraft disc braking system. In an ultra low-data regime of no more than twelve high-fidelity samples, multifidelity linear regression achieves approximately 2% – 12% improvement in median accuracy and a higher R 2 score relative to single-fidelity methods at comparable computational cost.

data augmentation↗
DOE OSTI2024

MATSE: Multi-fidelity assisted time-series emulation

I am going to present my work on multifidelity timeseries models at MS&T in Pittsburgh. We develop efficient machine learning methodologies to accelerate time-series predictions from a hierarchy of complex physics-based models.

Katona, Ryan Michael↗