Search NASA⌕ Search

SEARCH · Search NASA

Results for “multifidelity”

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 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 OSTI2021

A multifidelity method for a nonlocal diffusion model

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. In this work, we introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

Here, we study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Effectively using multifidelity optimization for wind turbine design

Abstract. Wind turbines are complex multidisciplinary systems that are challenging to design because of the tightly coupled interactions between different subsystems. Computational modeling attempts to resolve these couplings so we can efficiently explore new wind turbine systems early in the design process. Low-fidelity models are computationally efficient but make assumptions and simplifications that limit the accuracy of design studies, whereas high-fidelity models capture more of the actual physics but with increased computational cost. This paper details the use of multifidelity methods for optimizing wind turbine designs by using information from both low- and high-fidelity models to find an optimal solution at reduced cost. Specifically, a trust-region approach is used with a novel corrective function built from a nonlinear surrogate model. We find that for a diverse set of design problems – with examples given in rotor blade geometry design, wind turbine controller design, and wind power plant layout optimization – the multifidelity method finds the optimal design using 38 %–58 % of the computational cost of the high-fidelity-only optimization. The success of the multifidelity method in disparate applications suggests that it could be more broadly applied to other wind energy or otherwise generic applications.

17 WIND ENERGY↗
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 OSTI2021

MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources

We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data—we can combine noisy, non-nested evaluations of the information sources. Finally, numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces

Here, this paper focuses on the development of multifidelity modeling approaches using neural network surrogates, where training data arising from multiple model forms and resolutions are integrated to predict high-fidelity response quantities of interest at lower cost. We focus on the context of quantum chemistry and the integration of information from multiple levels of theory. Important foundations include the use of symmetry function-based atomic energy vector constructions as feature vectors for representing structures across families of molecules and single-fidelity neural network training capabilities that learn the relationships needed to map feature vectors to potential energy predictions. These foundations are embedded within several multifidelity topologies that decompose the high-fidelity mapping into model-based components, including sequential formulations that admit a general nonlinear mapping across fidelities and discrepancy-based formulations that presume an additive decomposition. Methodologies are first explored and demonstrated on a pair of simple analytical test problems and then deployed for potential energy prediction for C 5 H 5 using B2PLYP-D3/6-311++G(d,p) for high-fidelity simulation data and Hartree–Fock 6-31G for low-fidelity data. For the common case of limited access to high-fidelity data, our computational results demonstrate that multifidelity neural network potential energy surface constructions achieve roughly an order of magnitude improvement, either in terms of test error reduction for equivalent total simulation cost or reduction in total cost for equivalent error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Design and Analysis of Multifidelity Finite Element Simulations

Abstract The numerical accuracy of finite element analysis (FEA) depends on the number of finite elements used in the discretization of the space, which can be varied using the mesh size. The larger the number of elements, the more accurate the results are. However, the computational cost increases with the number of elements. In current practice, the experimenter chooses a mesh size that is expected to produce a reasonably accurate result, and for which the computer simulation can be completed in a reasonable amount of time. Improvements to this approach have been proposed using multifidelity modeling by choosing two or three mesh sizes. However, mesh size is a continuous parameter, and therefore, multifidelity simulations can be performed easily by choosing a different value for the mesh size for each of the simulations. In this article, we develop a method to optimally find the mesh sizes for each simulation and satisfy the same time constraints as a single or a double mesh size experiment. A range of different mesh sizes used in the proposed method allows one to fit multifidelity models more reliably and predict the outcome when meshes approach infinitesimally small, which is impossible to achieve in actual simulations. We illustrate our approach using an analytical function and a cantilever beam finite element analysis experiment.

Engineering↗
DOE OSTI2018

Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices

Variance-based sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be sufficiently accurate can make these analyses intractable when the model is expensive. This paper presents a multifidelity approach for estimating sensitivity indices that leverages cheaper low-fidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convection-diffusion-reaction model that demonstrate up to $10\times$ speedups for fixed convergence levels. Finally, for the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Exploration of multifidelity UQ sampling strategies for computer network applications.

Network modeling is a powerful tool to enable rapid analysis of complex systems that can be challenging to study directly using physical testing. Here, two approaches are considered: emulation and simulation. The former runs real software on virtualized hardware, while the latter mimics the behavior of network components and their interactions in software. Although emulation provides an accurate representation of physical networks, this approach alone cannot guarantee the characterization of the system under realistic operative conditions. Operative conditions for physical networks are often characterized by intrinsic variability (payload size, packet latency, etc.) or a lack of precise knowledge regarding the network configuration (bandwidth, delays, etc.); therefore uncertainty quantification (UQ) strategies should be also employed. UQ strategies require multiple evaluations of the system with a number of evaluation instances that roughly increases with the problem dimensionality, i.e., the number of uncertain parameters. It follows that a typical UQ workflow for network modeling based on emulation can easily become unattainable due to its prohibitive computational cost. In this paper, a multifidelity sampling approach is discussed and applied to network modeling problems. The main idea is to optimally fuse information coming from simulations, which are a low-fidelity version of the emulation problem of interest, in order to decrease the estimator variance. By reducing the estimator variance in a sampling approach it is usually possible to obtain more reliable statistics and therefore a more reliable system characterization. Several network problems of increasing difficulty are presented. For each of them, the performance of the multifidelity estimator is compared with respect to the single fidelity counterpart, namely, Monte Carlo sampling. For all the test problems studied in this work, the multifidelity estimator demonstrated an increased efficiency with respect to MC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

On-line Generation and Error Handling for Surrogate Models within Multifidelity Uncertainty Quantification

Uncertainty quantification is recognized as a fundamental task to obtain predictive numerical simulations. However, many realistic engineering applications require complex and computationally expensive high-fidelity numerical simulations for the accurate characterization of the system responses. Moreover, complex physical models and extreme operative conditions can easily lead to hundreds of uncertain parameters that need to be propagated through high-fidelity codes. Under these circumstances, a single fidelity approach, i.e. a workflow that only uses high-fidelity simulations to perform the uncertainty quantification task, is unfeasible due to the prohibitive overall computational cost. In recent years, multifidelity strategies have been introduced to overcome this issue. The core idea of this family of methods is to combine simulations with varying levels of fidelity/accuracy in order to obtain the multifidelity estimators or surrogates with the same accuracy of their single fidelity counterparts at a much lower computational cost. This goal is usually accomplished by defining a prioria sequence of discretization levels or physical modeling assumptions that can be used to decrease the complexity of a numerical realization and thus its computational cost. However ,less attention has been dedicated to low-fidelity models that can be built directly from the small number of high-fidelity simulations available. In this work we focus our attention on Reduced-Order Models that can be considered a particular class of data-driven approaches. Our main goal is to explore the combination of multifidelity uncertainty quantification and reduced-order models to obtain an efficient framework for propagating uncertainties through expensive numerical codes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2018

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport concept. An approach based on point-collocation, non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected using multiple higher-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability and potential computational savings of the multifidelity polynomial chaos approach, two model problems were explored. The first was a supersonic airfoil with three levels of modeling fidelity, each capturing a gradual increase in modeling of the underlying flow physics. As much as 50% computational cost reduction was observed using the mutlifidelity approach, while predicting nearly the same amount of uncertainty in drag. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Results of this analysis yielded nearly a 70% computational savings to predict a comparable amount of uncertainty in ground noise. Both problems illustrate the applicability and significant computational savings of the multifidelity method for efficient and accurate uncertainty quantification.

Thomas K. West IV↗
NASA NTRS2018

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport. An approach based on non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected by any number of high-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability of the multifidelity polynomial chaos approach, two model problems were explored. The first was supersonic airfoil with three levels of modeling fidelity, each capturing an additional level of physics. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Both problems illustrate the applicability and significant computational savings of the multifidelity polynomial chaos method.

West, Thomas K., IV↗
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 OSTI2022

Active learning with multifidelity modeling for efficient rare event simulation

Here, while multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies (including some high-dimensional problems) and two finite element model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

42 ENGINEERING↗
DOE OSTI2019

Multifidelity Information Fusion with Machine Learning: A Case Study of Dopant Formation Energies in Hafnia

Cost versus accuracy trade-offs are frequently encountered in materials science and engineering, where a particular property of interest can be measured/computed at different levels of accuracy or fidelity. Naturally, the most accurate measurement is also the most resource and time intensive, while the inexpensive quicker alternatives tend to be noisy. In such situations, a number of machine learning (ML) based multifidelity information fusion (MFIF) strategies can be employed to fuse information accessible from varying sources of fidelity and make predictions at the highest level of accuracy. In this work, we perform a comparative study on traditionally employed single-fidelity and three MFIF strategies, namely, (1) Δ-learning, (2) low-fidelity as a feature, and (3) multifidelity cokriging (CK) to compare their relative prediction accuracies and efficiencies for accelerated property predictions and high throughput chemical space explorations. We perform our analysis using a dopant formation energy data set for hafnia, which is a well-known high- k material and is being extensively studied for its promising ferroelectric, piezoelectric, and pyroelectric properties. We use a dopant formation energy data set of 42 dopants in hafnia—each studied in six different hafnia phases—computed at two levels of fidelities to find merits and limitations of these ML strategies. The findings of this work indicate that the MFIF based learning schemes outperform the traditional SF machine learning methods, such as Gaussian process regression and CK provides an accurate, inexpensive and flexible alternative to other MFIF strategies. While the results presented here are for the case study of hafnia, they are expected to be general. Furthermore, materials discovery problems that involve huge chemical space explorations can be studied efficiently (or even made feasible in some situations) through a combination of a large number of low-fidelity and a few high-fidelity measurements/computations, in conjunction with the CK approach.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Toward Accelerating Discovery via Physics-Driven and Interactive Multifidelity Bayesian Optimization

Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and often nondifferentiable parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, processing spaces, and molecular embedding spaces. Often these systems are expensive or time consuming to evaluate a single instance, and hence classical approaches based on exhaustive grid or random search are too data intensive. This resulted in strong interest toward active learning methods such as Bayesian optimization (BO) where the adaptive exploration occurs based on human learning (discovery) objective. However, classical BO is based on a predefined optimization target, and policies balancing exploration and exploitation are purely data driven. In practical settings, the domain expert can pose prior knowledge of the system in the form of partially known physics laws and exploration policies often vary during the experiment. Here, we propose an interactive workflow building on multifidelity BO (MFBO), starting with classical (data-driven) MFBO, then expand to a proposed structured (physics-driven) structured MFBO (sMFBO), and finally extend it to allow human-in-the-loop interactive interactive MFBO (iMFBO) workflows for adaptive and domain expert aligned exploration. These approaches are demonstrated over highly nonsmooth multifidelity simulation data generated from an Ising model, considering spin–spin interaction as parameter space, lattice sizes as fidelity spaces, and the objective as maximizing heat capacity. Detailed analysis and comparison show the impact of physics knowledge injection and real-time human decisions for improved exploration with increased alignment to ground truth. Here, the associated notebooks allow to reproduce the reported analyses and apply them to other systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗