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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

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthal resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Computational design of metamaterials with self contact

Inverse homogenization in combination with contact modeling, topology optimization and shape optimization is used to design metamaterials with optimized macroscopic response. The homogenization assumes length scale separation which allows the non-linear macroscopic behavior to be obtained by analyzing a single unit cell in a lattice structure. Self contact in the unit cell, which is modeled using a third medium contact method, is leveraged to obtain a complex homogenized response. The inverse homogenization problem is initially formulated as a topology optimization problem, where the macroscopic stress–strain behavior is tuned to our liking. However, it is well known that boundary phenomena are difficult to model in topology optimization and that interface modeling is crucial to accurately analyze contact. For that reason, the boundary representation of the topology optimized design is extracted and used as initial design in a subsequent shape optimization. The behaviors of our designs are verified by performing rigorous post-processing analyzes using conforming meshes and conventional contact formulations.

42 ENGINEERING↗
DOE OSTI2026

Uncertainty quantification for inverse problems with application to ptychographic reconstruction

Inverse problems in imaging are commonly solved by optimization or learned surrogates that return a single reconstruction, while uncertainty information is often unavailable. In many experimental settings, however, uncertainty is required to assess reliability, guide downstream analysis, and prioritize additional measurements. In this note, we present a compact uncertainty-quantification framework based on local objective curvature, and then specialize it to ptychographic reconstruction. We further show how repeated reconstructions can be aggregated in a statistically principled way, including a practical implementation path for PtychoNN.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Multiphysics analysis of liquid metal annular linear induction pumps: A project overview

Liquid metal-cooled fission reactors are both moderated and cooled by a liquid metal solution. These reactors are typically very compact and they can be used in regular electric power production, for naval and space propulsion systems or in fission surface power systems for planetary exploration. The coupling between the electromagnetics and thermo-fluid mechanical phenomena observed in liquid metal thermo-magnetic systems for nuclear and space applications gives rise to complex engineering magnetohydrodynamics and numerical problems. It is known that electromagnetic pumps have a number of advantages over rotating mechanisms: absence of moving parts, low noise and vibration level, simplicity of flow rate regulation, easy maintenance and so on. However, while developing annular linear induction pumps, we are faced with a significant problem of magnetohydrodynamic instability arising in the device. The complex flow behavior in this type of devices includes a time-varying Lorentz force and pressure pulsation due to the time-varying electromagnetic fields and the induced convective currents that originates from the liquid metal flow, leading to instability problems along the device geometry. The determinations of the geometry and electrical configuration of liquid metal thermo-magnetic devices give rise to a complex inverse magnetohydrodynamic field problem were techniques for global optimization should be used, magnetohydrodynamics instabilities understood –or quantified- and multiphysics models developed and analyzed. Lastly, we present a project overview as well as a few computational models developed to study liquid metal annular linear induction pumps using first principles and the a few results of our multi-physics analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Roundtable on Producing and Managing Large Scientific Data with Artificial Intelligence and Machine Learning (Brochure)

The US Department of Energy’s (DOE’s) twelve Basic Energy Sciences (BES) scientific user facilities provide access to the world’s most advanced research instruments, annually serving over 16,000 users with impact reported in nearly 7,000 publications and producing unprecedented quantities of scientific data. While impressive, reaching the full potential of these rapidly growing facilities will require new innovations to solve a variety of technical challenges in data acquisition, control, modeling, and analysis. Artificial intelligence and machine learning (AI/ML) have opened corresponding new avenues in optimization, efficient surrogate models, data analytics, and inverse problems. These intriguing capabilities suggest that AI/ML can greatly accelerate the quest to probe and understand fundamental phenomena across a vast range of lengths and timescales, potentially leading to transformative advances across scientific disciplines.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Visualizing and improving the robustness of phase retrieval algorithms

Coherent x-ray diffractive imaging is a novel imaging technique that utilizes phase retrieval and nonlinear optimization methods to image matter at nanometer scales. We explore how the convergence properties of a popular phase retrieval algorithm, Fienup's HIO, behave by introducing a reduced dimensionality problem allowing us to visualize and quantify convergence to local minima and the globally optimal solution. We then introduce generalizations of HIO that improve upon the original algorithm's ability to converge to the globally optimal solution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

15 GEOTHERMAL ENERGY↗
DOE OSTI2016

Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements and why current quantum annealing technology limits the size of problem that can be successfully solved today. Here, the formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Isopod (inverse Optimization And Design): Moose-based Application For Performing Inverse Optimization On Multiphysics Modeling And Simulation

ISOPOD (InverSe OPtimizatiOn and Design) will be a MOOSE (Multiphysics Object Oriented Simulation Environment)-based framework which will iteratively estimate the parameters by minimizing the difference between simulated and experimental observables. While inverse optimization has long been used for parameter estimation, the unique feature of ISOPOD is rapid solution of new inverse problems, leading to accelerated Research, Development and Demonstration (RD&D) for complex parameter estimation problems. This will be achieved by extending the software structure of MOOSE to inverse optimization, as well as building on the unique automatic differentiation feature of MOOSE.

Munday, LynnB↗
DOE OSTI2022

Bayesian optimization for inverse calibration of expensive computer models: A case study for Johnson-Cook model in machining

Inverse model calibration for identifying the constitutive model parameters can be computationally demanding for expensive-to-evaluate simulation models. Here, this paper presents a modified Bayesian optimization (BO) method, denoted as BO-bound, that incorporates theoretical bounds on the quantity of interest. A case study for the inverse calibration of the Johnson Cook (J-C) flow stress model parameters is presented using machining (cutting) force data. The results show fast calibration of the five J-C parameters within 25 simulations. In general, the BO-bound method is applicable for inverse calibration of any expensive simulation models as well as optimization problems with known bounds.

Bayesian optimization↗
DOE OSTI2022

Kinetics-Informed Neural Networks

Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize feed-forward artificial neural networks as basis functions to solve ordinary differential equations (ODEs) constrained by differential algebraic equations (DAEs) that describe microkinetic models (MKMs). We present an algebraic framework for the mathematical description and classification of reaction networks, types of elementary reaction, and chemical species. Under this framework, we demonstrate that the simultaneous training of neural nets and kinetic model parameters in a regularized multi-objective optimization setting leads to the solution of the inverse problem through the estimation of kinetic parameters from synthetic experimental data. We analyze a set of scenarios to establish the extent to which kinetic parameters can be retrieved from transient kinetic data, and assess the robustness of the methodology with respect to statistical noise. Furthermore, this approach to inverse kinetic ODEs can assist in the elucidation of reaction mechanisms based on transient data.

36 MATERIALS SCIENCE↗
DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗
DOE OSTI2021

Stellar and Accretion Disk Parameters of the Close Binary HD 50526

We present a photometric and spectroscopic study of HD 50526, an ellipsoidal binary member of the group Double Periodic Variable stars. Performing data mining in photometric surveys and conducting new spectroscopic observations with several spectrographs during 2008–2015, we obtained orbital and stellar parameters of the system. The radial velocities were analyzed with the genetic PIKAIA algorithm, whereas Doppler tomography maps for the Hα and Hβ lines were constructed with the Total Variation Minimization code. An optimized simplex algorithm was used to solve the inverse problem adjusting the light curve with the best stellar parameters for the system. We find an orbital period of 6.ͩ701 ± 0.ͩ001 and a long photometric cycle of 191 ± 2 days. We detected the spectral features of the coldest star and modeled it with a logg=2.79±0.02 dex giant of mass 1.13 ± 0.02 M {sub ⊙} and effective temperature 10500 ± 125 K. In addition, we determine a mass ratio q = 0.206 ± 0.033 and that the hot star is a B-type dwarf of mass 5.48 ± 0.02 M {sub ⊙}. The V-band orbital light curve can be modeled including the presence of an accretion disk around the hotter star. This fills the Roche lobe of the hotter star and has a radius 14.74 ± 0.02 R {sub ⊙} and the temperature at the outer edge is 9400 K. Two bright spots located in the disk account for the global morphology of the light curve. The Doppler tomography maps of Hα and Hβ reveal complex structures of mass fluxes in the system.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Machine Learning assisted optimization and parameter space exploration dataset of spin ice Hamiltonian

This repository contains both simulated and experimental structure factor data for the data challenge involving the inverse scattering problem. The simulated data were generated during a machine-learning-assisted optimization routine described in ref[1]. The experimental structure factor was measured on a rare-earth oxide, Dy2Ti2O7 using diffuse neutron scattering from time-of-flight techniques on the CORELLI instrument at the Spallation Neutron Source, Oak Ridge National Laboratory. A Metropolis Monte Carlo code implemented to run in a High-performance computing setting was used to calculated simulated structure factors for the spin-ice Hamiltonian at 680 mK, which is the same temperature as for the experimental data. The total size of all the files in this repository is 5.12 GB. A detailed description of the files is given below. ExperimentalData_630mK.dat – A linearized version of 3-dimensional experimental data of size 61×81×21. This data was processed to remove an estimation of non-magnetic background, including nuclear scattering signal and instrumentation background. Parameters.dat – 6700 samples were evaluated over the 4-dimensional parameter space (J_1, J_2, J_3 and J_(3^' )). There is an additional parameter, D in the spin Hamiltonian to mimic the dipolar interaction between magnetic ions. However, this parameter, D was fixed to a value determined by prior work. This file contains five columns for the parameters J_1, J_2, J_3, J_(3^' ) and D respectively. 3D_Simulation_Data.dat – The simulated structure factor, S(Q) data are included in this file. Each raw contains a linearized array of 3D volumes of S(Q) calculated for the parameter set given in the corresponding row of the file Parameters.dat. The size of the volume data was matched to the experimental data. Qx(h,-h,0).dat, Qy(k,k,-2k).dat, Qz(l,l,l).dat – These files contain the h, k, and l values along with the reciprocal vectors [h,-h,0], [k,k,-2k] and [l,l,l] respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2023

On unifying randomized methods for inverse problems

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a sample average approximation (SAA). More importantly, we are able to prove a single theoretical result that guarantees the asymptotic convergence for a variety of randomized methods. Additionally, viewing randomized methods as an SAA enables us to prove, for the first time, a single non-asymptotic error result that holds for randomized methods under consideration. Another important consequence of our unified framework is that it allows us to discover new randomization methods. Here, we present various numerical results for linear, nonlinear, algebraic, and PDE-constrained inverse problems that verify the theoretical convergence results and provide a discussion on the apparently different convergence rates and the behavior for various randomized methods.

42 ENGINEERING↗
DOE OSTI2020

Bi-fidelity Gradient-Based Approach for Nonlinear Well Logging Inverse Problems

Solving a non-linear inverse problem is challenging in computational science and engineering. Sampling based methods require a large number of model valuations; gradientbased methods require fewer model evaluations but only find the local minima. Multifidelity optimization combines the low fidelity model and the high-fidelity model to achieve both high accuracy and high efficiency. In this paper, we present a bi-fidelity approach to solve non-linear inverse problems. In the bi-fidelity inversion method, the low-fidelity model is used to acquire a good initial guess, and the high-fidelity model is used to locate the global minimum. Combined with a multi-start optimization scheme, the proposed approach significantly increases the possibility of finding the global minimum for nonlinear inverse problems with many local minima. The method is tested with two toy problems and then applied to an electromagnetic well logging inverse problem, which is difficult to solve using traditional gradient-based methods. The bi-fidelity method provides promising inversion results and can be easily applied to traditional gradient-based methods.

42 ENGINEERING↗
DOE OSTI2017

A scalable design of experiments framework for optimal sensor placement

Here, we present a scalable design of an experiments framework for sensor placement in systems described by partial differential equations (PDEs). In particular, we aim to compute optimal sensor locations by minimizing the uncertainty of parameters estimated from Bayesian inverse problems and where the system. The resulting problem is a computationally intractable mixed-integer nonlinear program constrained by PDEs. We approach this problem with two heuristics used in compressed sensing and optimal control literature: a sparsity-inducing approach and a sum-up rounding approach. We also investigate metrics to guide the design of experiments (the total flow variance and the A-optimal design criterion) and analyze the effect of different noise structures (white and colored). Using an application in natural gas pipelines, we conclude that the sum-up rounding approach approach gives the best results and produces shrinking gaps with increasing mesh resolution. We also observe that convergence for the white noise measurement error case is slower than for the colored noise case. For A-optimal design, the solution is close to a uniform distribution of sensors along the pipeline while for the flow variance design the distribution is unstructured.

42 ENGINEERING↗