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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Robust and scalable uncertainty estimation with conformal prediction for machine-learned interatomic potentials

Abstract Uncertainty quantification (UQ) is important to machine learning (ML) force fields to assess the level of confidence during prediction, as ML models are not inherently physical and can therefore yield catastrophically incorrect predictions. Established a-posteriori UQ methods, including ensemble methods, the dropout method, the delta method, and various heuristic distance metrics, have limitations such as being computationally challenging for large models due to model re-training. In addition, the uncertainty estimates are often not rigorously calibrated. In this work, we propose combining the distribution-free UQ method, known as conformal prediction (CP), with the distances in the neural network’s latent space to estimate the uncertainty of energies predicted by neural network force fields. We evaluate this method (CP+latent) along with other UQ methods on two essential aspects, calibration, and sharpness, and find this method to be both calibrated and sharp under the assumption of independent and identically-distributed (i.i.d.) data. We show that the method is relatively insensitive to hyperparameters selected, and test the limitations of the method when the i.i.d. assumption is violated. Finally, we demonstrate that this method can be readily applied to trained neural network force fields with traditional and graph neural network architectures to obtain estimates of uncertainty with low computational costs on a training dataset of 1 million images to showcase its scalability and portability. Incorporating the CP method with latent distances offers a calibrated, sharp and efficient strategy to estimate the uncertainty of neural network force fields. In addition, the CP approach can also function as a promising strategy for calibrating uncertainty estimated by other approaches.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

B-PINNs: Bayesian Physics-informal Neural Networks for Forward and Inverse PDE Problems with Noisy Data

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior. B-PINNs make use of both physical laws and scattered noisy measurements to provide predictions and quantify the aleatoric uncertainty arising from the noisy data in the Bayesian framework. Compared with PINNs, in addition to uncertainty quantification, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting. We conduct a systematic comparison between the two different approaches for the B-PINNs posterior estimation (i.e., HMC or VI), along with dropout used for quantifying uncertainty in deep neural networks. Our experiments show that HMC is more suitable than VI with mean field Gaussian approximation for the B-PINNs posterior estimation, while dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty. Finally, we replace the BNN in the prior with a truncated Karhunen-Loève (KL) expansion combined with HMC or a deep normalizing flow (DNF) model as posterior estimators. The KL is as accurate as BNN and much faster but this framework cannot be easily extended to high-dimensional problems unlike the BNN based framework.

Non linear PDEs, Noisy data, Bysian physics inform↗
DOE OSTI2021

A TTL-based Approach for Content Placement in Edge Networks

Edge networks are promising to provide better services to users by provisioning computing and storage resources at the edge of networks. However, due to the uncertainty and diversity of user interests, content popularity, distributed network structure, cache sizes, it is challenging to decide where to place the content, and how long it should be cached. In this paper, we study the utility optimization of content placement at edge networks through timer-based (TTL) policies. We propose provably optimal distributed algorithms that operate at each network cache to maximize the overall network utility. Our TTL-based optimization model provides theoretical answers to how long each content must be cached, and where it should be placed in the edge network. Extensive evaluations show that our algorithm significantly outperforms path replication with conventional caching algorithms over some network topologies.

Panigrahy, Nitish K.↗
DOE OSTI2021

A comparison of Gaussian processes and neural networks for computer model emulation and calibration

The Department of Energy relies on complex physics simulations for prediction in domains like cosmology, nuclear theory, and materials science. These simulations are often extremely computationally intensive, with some requiring days or weeks for a single simulation. In order to assure their accuracy, these models are calibrated against observational data in order to estimate inputs and systematic biases. Because of their great computational complexity, this process typically requires the construction of an emulator, a fast approximation to the simulation. In this paper, two emulator approaches are compared: Gaussian process regression and neural networks. Their emulation accuracy and calibration performance on three real problems of Department of Energy interest is considered. On these problems, the Gaussian process emulator tends to be more accurate with narrower, but still well-calibrated uncertainty estimates. The neural network emulator is accurate, but tends to have large uncertainty on its predictions. Finally, as a result, calibration with the Gaussian process emulator produces more constrained posteriors that still perform well in prediction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Here we analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify time-dependent parameters and data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and fractional-order and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks. In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by neural networks. We investigate the structural and practical identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with neural networks and with control measures in forecasting the pandemic.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

An adaptive, data-driven multiscale approach for dense granular flows

The accuracy of coarse-grained continuum models of dense granular flows is limited by the lack of high-fidelity closure models for granular rheology. One approach to addressing this issue, referred to as the hierarchical multiscale method, is to use a high-fidelity fine-grained model to compute the closure terms needed by the coarse-grained model. The difficulty with this approach is that the overall model can become computationally intractable due to the high computational cost of the high-fidelity model. In this work, we describe a multiscale modeling approach for dense granular flows that utilizes neural networks trained using high-fidelity discrete element method (DEM) simulations to approximate the constitutive granular rheology for a continuum incompressible flow model. Our approach leverages an ensemble of neural networks to estimate predictive uncertainty that allows us to determine whether the rheology at a given point is accurately represented by the neural network model. Additional DEM simulations are only performed when needed, minimizing the number of additional DEM simulations required when updating the rheology. This adaptive coupling significantly reduces the overall computational cost of the approach while controlling the error. In addition, the neural networks are customized to learn regularized rheological behavior to ensure well-posedness of the continuum solution. We first validate the approach using two-dimensional steady-state and decelerating inclined flows. We then demonstrate the efficiency of our approach by modeling three-dimensional sub-aerial granular column collapse for varying initial column aspect ratios, where our multiscale method compares well with the computationally expensive computational fluid dynamics (CFD)-DEM simulation.

Dense granular flows↗
DOE OSTI2023

Deducing the EOS of dense neutron star matter with machine learning

Abstract The interior of a neutron star is a unique astrophysical laboratory for studying matter at extreme densities and pressures beyond what is replicable in terrestrial experiments. While there is no direct way to simulate the interior of these stars, one promising avenue to learning more about the equation of state (EOS) of such matter is through X‐rays emitted from the star's surface. The current state‐of‐the‐art method for inference of EOS from a star's X‐ray spectra uses piece‐wise, simulation‐based likelihoods that rely on theoretical assumptions complicated by systematic uncertainties. To reduce the dimensionality of the problem, this method infers macroscopic properties of the star (mass and radius) from emitted X‐ray spectra, and from those quantities infers the EOS. This work approaches the same problem using machine learning techniques, demonstrating a series of enhancements to the current state‐of‐the‐art by realistic uncertainty quantification and reducing the need for theoretical assumptions. We also demonstrate novel inference of the EOS directly from high‐dimensional simulated X‐ray spectra from neutron stars that negate the need for a piece‐wise approach. This inference allows for a natural propagation of uncertainties from the X‐ray spectra by conditioning the discussed networks on realistic sources of uncertainty for each star.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Calibrating Bayesian generative machine learning for Bayesiamplification

Recently, combinations of generative and Bayesian deep learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated distribution originating from limited training statistics. The interpretation of a distribution-wide uncertainty however remains ill-defined. We show a clear scheme for quantifying the calibration of Bayesian generative machine learning models. For a Continuous Normalizing Flow applied to a low-dimensional toy example, we evaluate the calibration of Bayesian uncertainties from either a mean-field Gaussian weight posterior, or Monte Carlo sampling network weights, to gauge their behaviour on unsteady distribution edges. Well calibrated uncertainties can then be used to roughly estimate the number of uncorrelated truth samples that are equivalent to the generated sample and clearly indicate data amplification for smooth features of the distribution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

How to understand limitations of generative networks

Well-trained classifiers and their complete weight distributions provide us with a well-motivated and practicable method to test generative networks in particle physics. We illustrate their benefits for distribution-shifted jets, calorimeter showers, and reconstruction-level events. In all cases, the classifier weights make for a powerful test of the generative network, identify potential problems in the density estimation, relate them to the underlying physics, and tie in with a comprehensive precision and uncertainty treatment for generative networks.

Physics↗
DOE OSTI2022

Multimodel ensemble predictions of precipitation using bayesian neural networks

Multimodel ensembling improves predictions and considers model uncertainties. In this study, we present a Bayesian Neural Network (BNN) ensemble approach for large-scale precipitation predictions based on a set of climate models. BNN infers spatiotemporally varying model weights and biases through the calibration against observations. This ensemble scheme of BNN sufficiently leverages individual model skill for accurate predictions as well as provides interpretability about which models contribute more to the ensemble prediction at which locations and times to inform model development. Additionally, BNN accurately quantifies epistemic uncertainty to avoid overconfident projections. We demonstrate BNN’s superior prediction performance to three state-of-the-art ensemble approaches and discuss its interpretability and uncertainty quantification.

Fan, Patrick↗
DOE OSTI2022

Multimodel Ensemble Predictions of Precipitation using Bayesian Neural Networks

Multimodel ensembling improves predictions and considers model uncertainties. In this study, we present a Bayesian Neural Network (BNN) ensemble approach for large-scale precipitation predictions based on a set of climate models. BNN infers spatiotemporally varying model weights and biases through the calibration against observations. This ensemble scheme of BNN sufficiently leverages individual model skill for accurate predictions as well as provides interpretability about which models contribute more to the ensemble prediction at which locations and times to inform model development. Additionally, BNN accurately quantifies epistemic uncertainty to avoid overconfident projections. We demonstrate BNN’s superior prediction performance to three state-of-the-art ensemble approaches and discuss its interpretability and uncertainty quantification.

Fan, Patrick↗
DOE OSTI2024

Uncertainty quantification and propagation in lithium-ion battery electrodes using bayesian convolutional neural networks

The complex nature of manufacturing processes stipulates electrodes to possess high variability with increased heterogeneity during production. X-ray computed tomography imaging has proved to be critical in visualizing the complicated stochastic particle distribution of as-manufactured electrodes in lithium-ion batteries. However, accurate prediction of their electrochemical performance necessitates precise evaluation of kinetic and transport properties from real electrodes. Image segmentation that characterizes voxels to particle/pore phase is often meticulous and fraught with subjectivity owing to a myriad of unconstrained choices and filter algorithms. Here we utilize a Bayesian convolutional neural network to tackle segmentation subjectivity and quantify its pertinent uncertainties. Otsu inter-variance and Blind/Referenceless Imaging Spatial Quality Evaluator are used to assess the relative image quality of grayscale tomograms, thus evaluating the uncertainty in the derived microstructural attributes. We analyze how image uncertainty is correlated with the uncertainties and magnitude of kinetic and transport properties of an electrode, further identifying pathways of uncertainty propagation within microstructural attributes. The coupled effect of spatial heterogeneity and microstructural anisotropy on the uncertainty quantification of transport parameters is also understood. This work demonstrates a novel methodology to extract microstructural descriptors from real electrode images through quantification of associated uncertainties and discerning the relative strength of their propagation, thus facilitating feedback to manufacturing processes from accurate image based electrochemical simulations.

25 ENERGY STORAGE↗
DOE OSTI2024

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The Sensitivity of Variational Bayesian Neural Network Performance to Hyperparameters

In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs) produce predictive uncertainty by propagating uncertainty in neural network (NN) weights and offer the promise of obtaining not only an accurate predictive model but also accurate UQ. However, in practice, obtaining accurate UQ with BNNs is difficult due in part to the approximations used for model training (such as those made in variational inference) and in part to the need to choose a suitable set of hyperparameters; these hyperparameters outnumber those needed for traditional NNs and often have opaque effects on the results. We aim to shed light on the effects of hyperparameter choices for variational BNNs by performing a global sensitivity analysis of variational BNN performance under varying hyperparameter settings. Our results indicate that many of the hyperparameters interact with each other to affect both predictive accuracy and UQ. For improved usage of variational BNNs in real-world applications, we suggest that thorough hyperparameter tuning, including tuning of prior hyperparameters and loss function parameters, is essential for accurate UQ in variational BNNs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications

Abstract Robust quantification of predictive uncertainty is a critical addition needed for machine learning applied to weather and climate problems to improve the understanding of what is driving prediction sensitivity. Ensembles of machine learning models provide predictive uncertainty estimates in a conceptually simple way but require multiple models for training and prediction, increasing computational cost and latency. Parametric deep learning can estimate uncertainty with one model by predicting the parameters of a probability distribution but does not account for epistemic uncertainty. Evidential deep learning, a technique that extends parametric deep learning to higher-order distributions, can account for both aleatoric and epistemic uncertainties with one model. This study compares the uncertainty derived from evidential neural networks to that obtained from ensembles. Through applications of the classification of winter precipitation type and regression of surface-layer fluxes, we show evidential deep learning models attaining predictive accuracy rivaling standard methods while robustly quantifying both sources of uncertainty. We evaluate the uncertainty in terms of how well the predictions are calibrated and how well the uncertainty correlates with prediction error. Analyses of uncertainty in the context of the inputs reveal sensitivities to underlying meteorological processes, facilitating interpretation of the models. The conceptual simplicity, interpretability, and computational efficiency of evidential neural networks make them highly extensible, offering a promising approach for reliable and practical uncertainty quantification in Earth system science modeling. To encourage broader adoption of evidential deep learning, we have developed a new Python package, Machine Integration and Learning for Earth Systems (MILES) group Generalized Uncertainty for Earth System Science (GUESS) (MILES-GUESS) ( https://github.com/ai2es/miles-guess ), that enables users to train and evaluate both evidential and ensemble deep learning. Significance Statement This study demonstrates a new technique, evidential deep learning, for robust and computationally efficient uncertainty quantification in modeling the Earth system. The method integrates probabilistic principles into deep neural networks, enabling the estimation of both aleatoric uncertainty from noisy data and epistemic uncertainty from model limitations using a single model. Our analyses reveal how decomposing these uncertainties provides valuable insights into reliability, accuracy, and model shortcomings. We show that the approach can rival standard methods in classification and regression tasks within atmospheric science while offering practical advantages such as computational efficiency. With further advances, evidential networks have the potential to enhance risk assessment and decision-making across meteorology by improving uncertainty quantification, a longstanding challenge. This work establishes a strong foundation and motivation for the broader adoption of evidential learning, where properly quantifying uncertainties is critical yet lacking.

Schreck, John S.↗