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Results for “Inverse uncertainty quantification”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion

SUMMARY Full-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

58 GEOSCIENCES↗
DOE OSTI2017

Application of Polynomial Chaos Expansion in One-Dimensional Inverse Transport Problems

In the problem of inverse radiation transport, measurements of particle leakages from radioactive source/shield systems are used to infer unknown parameters within the systems. This reconstruction can be accomplished by finding the physical parameters of the unknown system that minimize the difference between calculated detector responses and measured detector responses. The inverse transport solver should also propagate uncertainties from the detector responses to the reconstructed parameter values. Recently, the Differential Evolution Adaptive Metropolis (DREAM) method was shown to be a robust method for uncertainty quantification in inverse problems. The DREAM method uses the differential evolution algorithm to choose efficient steps in a Markov chain Monte Carlo (MCMC) simulation. Although the DREAM method has been shown to be more efficient than traditional MCMC approaches, it still requires thousands of transport computations to accurately quantify uncertainty. For the simple ray-tracing model, it was possible to perform these calculations in a reasonable amount of time (under an hour). However, inverse transport problems that require computationally-intensive transport solvers will need prohibitively long run times when using the DREAM method. A way to overcome the computational burden of the DREAM method is to perform surrogate modeling using the polynomial chaos expansion (PCE) approach. It was recently shown that the PCE method provides both accurate and computationally inexpensive uncertainty quantification in forward radiation source/shield problems. PCE was also recently applied to an inverse problem in nonlinear point reactor kinetics within a standard MCMC approach. PCE was first used with the DREAM method where it was applied to inverse problems in groundwater modeling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Scalable Multilevel Uncertainty Quantification Concepts for Extreme-Scale Multiscale Problems

Our work in this project is aimed at making fundamental advances in multilevel and multiscale methods for problems with uncertainties related to flows in porous media. The main thrust of this research is to develop a systematic multiscale, multilevel parallel approaches for problems with uncertainties and use them in the uncertainty quantification. A key emphasis is on problems without an apparent scale separation in space, time, and uncertainty spaces. Multiscale solution methods are currently under active investigation. However, the develop- ment of multiscale methods for problems with uncertainties where the scales and uncertainties are tightly coupled is a research area that is less explored. During this project, we have made some significant contributions to the developments of multiscale methods, the uncertainty quantification for multiscale methods, multiscale model learning, uncertainty quantification in inverse problems, and applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A staged deep learning approach to spatial refinement in 3D temporal atmospheric transport

High-resolution spatiotemporal simulations effectively capture the complexities of atmospheric plume dispersion in complex terrain. However, their high computational cost makes them impractical for applications requiring rapid responses or iterative processes, such as optimization, uncertainty quantification, or inverse modeling. To address this challenge, this work introduces the Dual-Stage Temporal Three-dimensional UNet Super-resolution (DST3D-UNet-SR) model, a highly efficient deep learning model for plume dispersion predictions. DST3D-UNet-SR is composed of two sequential modules: the temporal module (TM), which predicts the transient evolution of a plume in complex terrain from low-resolution temporal data, and the spatial refinement module (SRM), which subsequently enhances the spatial resolution of the TM predictions. We train DST3D-UNet-SR using a comprehensive dataset derived from high-resolution large eddy simulations (LES) of plume transport. We propose the DST3D-UNet-SR model to significantly accelerate LES of three-dimensional (3D) plume dispersion by three orders of magnitude. Additionally, the model demonstrates the ability to dynamically adapt to evolving conditions through the incorporation of new observational data, substantially improving prediction accuracy in high-concentration regions near the source.

3D temporal sequences↗
DOE OSTI2017

Bayesian and variational Bayesian approaches for flows in heterogeneous random media

In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation technique decomposes the solution into the sum of separable functions (with respect to randomness and the space), where each term is calculated based on a variational approach. This is similar to Proper Generalized Decomposition (PGD). Next, we apply a multiscale technique to solve for each term (as in ) and, further, decompose the random function into 1D fields. As a result, our proposed method provides an approximation hierarchy for the solution as we increase the number of terms in the expansion and, also, increase the spatial resolution of each term. We use the hierarchical solution distributions in a variational Bayesian approximation to perform uncertainty quantification in the inverse problem. We conduct a detailed numerical study to explore the performance of the proposed uncertainty quantification technique and show the theoretical posterior concentration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.

Yang, Xiu↗
DOE OSTI2026

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗
DOE OSTI2023

Uncertainty Quantification for Multiphase Computational Fluid Dynamics Closure Relations with a Physics-Informed Bayesian Approach

Multiphase Computational Fluid Dynamics (MCFD) based on the two-fluid model is considered a promising tool to model complex two-phase flow systems. MCFD simulation can predict local flow features without resolving interfacial information. As a result, the MCFD solver relies on closure relations to describe the interaction between the two phases. Those empirical or semi-mechanistic closure relations constitute a major source of uncertainty for MCFD predictions. In this paper, we leverage a physics-informed uncertainty quantification (UQ) approach to inversely quantify the closure relations’ model form uncertainty in a physically consistent manner. This proposed approach considers the model form uncertainty terms as stochastic fields that are additive to the closure relation outputs. Combining dimensionality reduction and Gaussian processes, the posterior distribution of the stochastic fields can be effectively quantified within the Bayesian framework with the support of experimental measurements. As this UQ approach is fully integrated into the MCFD solving process, the physical constraints of the system can be naturally preserved in the UQ results. Here, in a case study of adiabatic bubbly flow, we demonstrate that this UQ approach can quantify the model form uncertainty of the MCFD interfacial force closure relations, thus effectively improving the simulation results with relatively sparse data support.

42 ENGINEERING↗
DOE OSTI2023

MrHyDE v.1.0

SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE is designed to enable moving beyond forward simulation for multiscale applications which includes optimization, control, uncertainty quantification, and stochastic inversion. The framework provides interfaces to several packages within the Trilinos framework and leverages automatic differentiation to enable adjoint capabilities for large-scale, gradient-based optimization. MrHyDE provides automated multiscale capabilities through a subgrid model interface and multiscale Dirichlet-to-Neumann maps. For extreme-scale applications, MrHyDE provides in situ data-compression algorithms to reduce memory requirements while maintaining performance. MrHyDE is a general-purpose, computational framework for the solution of multiscale and multiphysics applications. It uses a combination of structure-preserving, physics-compatible discretizations, fully implicit methods, multi-resolution schemes, or fully explicit methods. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2022

A refined assessment of nuclear data target accuracy requirements for ALFRED

The interest in target accuracy assessment has been recently renewed within the OECD/NEA Working Party on International Nuclear Data Evaluation Cooperation with an update exercise, thanks to the invaluable initiative of Massimo Salvatores. This work, moving from evaluations on the main core integral parameters of the Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED), and the identification of the associated target accuracies needed for improving its design, approaches the retrieval of target accuracy requirements for nuclear data, as the inverse problem of uncertainty quantification. The preliminary results obtained in a previous work are here refined by explicitly taking into account the total contribution due to correlations among variables in the optimization constraint, while its various components are evaluated individually. Moreover, three different sets of cost parameters are considered to introduce a bias in the solution in order to take in due account the relative difficulties in the execution of new differential experiments as needed for achieving the proposed target accuracies. By this, the obtained results are deemed usefully informative, and proposed for the update of a High Priority List which identifies the isotopes-reaction couples of most interest for future refinement experiments, especially when integrated with further analogous information collected on other advanced nuclear systems. Among the cross-sections whose refinement contributes the most to the reduction of the multiplication factor, the fission of Pu{sup 239} was found, which needs to be fixed below 1% in the range of interest for ALFRED (2 keV-4 MeV). Another contribution for the amelioration of the multiplication factor calculation accuracy, is due to the capture channel of Pu{sup 239}, for which the initial high uncertainty (around 15%) can be significantly reduced resorting to easily practicable experiments. The same occurs for the inelastic of Pb{sup 207}, for which the initial uncertainty value of around 50% can be drastically reduced up to target values between 4% and 7%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2019

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

DiaMonD is a multi-institutional DOE MMICC effort that aims to address the challenges of end-to-end, data-to-decisions modeling and simulation for complex computational science and engineering problems in a unified, systematic, and integrated fashion. Institutions involved are Colorado State, Florida State, Los Alamos, MIT, Oak Ridge, Stanford, and UT-Austin. The goals of DiaMonD are (1) to develop advanced mathematical methods and analysis for multimodel, multiphysics, multiscale model problems driven by frontier DOE applications, including those in subsurface energy and environmental flows, materials for energy storage and conversion, and ice sheet dynamics; (2) to create theory and algorithms for integrated inversion, optimization, and uncertainty quantification for these complex problems; and (3) to disseminate the philosophy of an integrated end-to-end, data-to-decisions approach to modeling and simulation of complex problems to the broader applied math and computational science communities through workshops and other outreach.

42 ENGINEERING↗
DOE OSTI2023

Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments

There is an increasing aspiration to utilize machine learning (ML) for various tasks of relevance to national security. ML models have thus far been mostly applied to tasks and domains that, while impactful, have sufficient volume of data. For predictive tasks of national security relevance, ML models of great capacity (ability to approximate nonlinear trends in input-output maps) are often needed to capture the complex underlying physics. However, scientific problems of relevance to national security are often accompanied by various sources of sparse and/or incomplete data, including experiments and simulations, across different regimes of operation, of varying degrees of fidelity, and include noise with different characteristics and/or intensity. State-of-the-art ML models, despite exhibiting superior performance on the task and domain they were trained on, may suffer detrimental loss in performance in such sparse data environments. This report summarizes the results of the Laboratory Directed Research and Development project entitled Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments. The objective of the project was to develop a new transfer learning (TL) framework that aims to adaptively blend the data across different sources in tackling one task of interest, resulting in enhanced trustworthiness of ML models for mission- and safety-critical systems. The proposed framework determines when it is worth applying TL and how much knowledge is to be transferred, despite uncontrollable uncertainties. The framework accomplishes this by leveraging concepts and techniques from the fields of Bayesian inverse modeling and uncertainty quantification, relying on strong mathematical foundations of probability and measure theories to devise new uncertainty-aware TL workflows.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

New approaches to Bayesian uncertainty quantification for Nuclear Science (Final Technical Report)

Inverse problems play a central role in experimentation and theory/data comparisons for many areas of modern Nuclear Physics (NP) and High-Energy Physics (HEP). Bayes’s Theorem is a powerful tool for solving Inverse Problems, providing conceptually transparent and unbiased constraints on theoretical parameters and their uncertainties (“Bayesian Inference”) and enabling the quantification of agreement or tension between models and data. However, analyses based on Bayesian Inference are often challenging for NP and HEP applications, either because of the large number of parameters in the problem, the high computational cost, or both. We propose a multi-institutional collaboration to develop and deploy novel Bayesian analysis tools that advance the scientific scope of a broad range of current and future NP experiments. This project brings together NP domain scientists working on several high-profile NP projects for which new, high-performance Bayesian Uncertainty Quantification (“Bayesian UQ”) methods are essential to carry out the science, and data scientists who are developing state-of-the-art methods applicable to these problems. The NP projects in this proposal comprise measurements of the mass and fundamental nature of the neutrino; study of the Quark-Gluon Plasma that filled the early universe; and mapping of natural and anthropogenic radiation environments. While these NP projects have very different scientific goals, with datasets and analysis approaches that differ significantly, they share common requirements for improving computationally intensive Bayesian analyses using advanced Machine Learning algorithms and will benefit strongly from a coherent effort to develop general solutions. This proposal brings together these projects and forefront ML-based data science algorithms to develop such general solutions. The methods developed in this project will also be more widely applicable, thereby advancing science in the larger Nuclear Physics portfolio.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Uncertainty Quantification in Reduced Order Modeling

Presentation describes research to analyze radiation transport using reduced order modeling as an alternate approach to Monte Carlo-based methods, with a goal of developing a variance reduction method that increases computing efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs

Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines. We address this challenge for the problem of modeling subsurface flow at the Hanford Site by combining stochastic computational models with observational data using physics-informed GAN models. The geographic extent, spatial heterogeneity, and multiple correlation length scales of the Hanford Site require training a computationally intensive GAN model to thousands of dimensions. We develop a highly optimized implementation that scales to {\herogpucount} NVIDIA Volta GPUs. We develop a hierarchical scheme based on a multi-player game-theoretic approach for exploiting domain parallelism, map discriminators and generators to multiple GPUs, and employ efficient communication schemes to ensure training stability and convergence. Our implementation scales to {\heronodecount} nodes on the Summit supercomputer with a \weakscalingeff\% scaling efficiency, achieving peak and sustained half-precision rates of {\heropeakperf} PF/s and {\herosustainedperf} PF/s.

physics informed ML, machine learning, generative ↗
DOE OSTI2023

Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems

We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.

Engineering↗