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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Problems of Nuclear Technology and Radiation Safety

This work discusses ethical issues arising in the course of the development of nuclear technologies and related issues of radiation safety. Attention is paid to ethical dilemmas and proposed solutions. The author suggests a critical analysis of the relevant discussions, conducted, first of all, in the English-language literature, and muses on the specifics associated with their transfer to the Russian context. This study considers ethical problems arising in context of the depletion of uranium resources and nuclear waste management and including the inevitable risks for the present and future generations, such as inter- and intragenerational justice (Gardiner's problem) and the problem of the identity of future generations (Parfit’s problem); problems of collectivity and individuality in the assessment of permissible radiation doses for workers at nuclear enterprises and the population associated with the need to combine deontological and utilitarian approaches in the practice of radiation protection. The author demonstrates cultural differences in attitudes towards the safety of the current and future generations of the population of countries and regions and the associated ambiguities in the choice of technology for nuclear reactors, long-term disposal or processing of nuclear waste; double standards in ensuring the radiation safety of personnel of nuclear facilities and the population; ethical problems of risk compensation to workers of radiation-hazardous production facilities; issues of gender differences in sensitivity to radiation exposure, gender equality and discrimination in relation to access to the labor market in the nuclear industry. The article elucidates the importance of socio-humanitarian discussion of the ethical problems of nuclear technologies and radiation safety Such debates currently are almost absent in the Russian-language philosophical literature, despite its exceptional importance due to both the level of development of nuclear energy in Russia and the potential risks that these technologies pose to current and future generations of both employees of nuclear facilities and the population of the country, neighboring countries, and the world. The purpose of this article, thus, is to initiate such a discussion.

ethics of science and technology↗
DOE OSTI2023

Designing interagency responses to wicked problems: A viable system model board game

Government agencies struggle to address wicked problems because they are open-ended, highly interdependent issues that cross agency, stakeholder, jurisdictional, and geopolitical boundaries. While both quantitative modelling and qualitative problem structuring methodologies have been used to support interagency decision making in the past, co-designing an effective interagency organization to collaboratively tackle wicked problems is more challenging. Few approaches have been developed to enable such efforts. This paper explains how the viable system model (VSM) was implemented through a board game, which was employed to co-design an interagency meta-organization that would be capable of more effectively collaborating to jointly address a wicked problem: international organized drug crime and its interface with local gangs in Chicago, USA. The board game was developed to make the VSM easier for the participants to learn, given that the cybernetic language and engineering-influenced diagrams in the original literature can be off-putting to leaders and managers. The board game was used as the final stage of a multi-method, systemic approach, which involved boundary critique and problem structuring as well as deployment of the VSM. The research findings indicate that the VSM board game, used as part of a larger mixed-methods systemic intervention, contributes to building trust in the value of systems thinking amongst the participants, and sets up a rich context for collaboration on multi-agency co-design. The game therefore offers significant promise as part of the co-design of interagency responses to wicked problems because it creates an embodied process for stakeholders to learn about the VSM. It also reduces the work involved in this learning. Thus, the game enables an effective appropriation of the VSM language and criteria.

Business & Economics↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗
DOE OSTI2020

Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2023

Enabling Hyper-Differential Sensitivity Analysis for Ill-Posed Inverse Problems

Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high dimensionality of the parameters and computational complexity of the PDE solves make such problems challenging. A common approach is to reduce the dimension by fixing some parameters (which we will call auxiliary parameters) to a best estimate and use techniques from PDE-constrained optimization to estimate the other parameters. In this article, hyper-differential sensitivity analysis (HDSA) is used to assess the sensitivity of the solution of the PDE-constrained optimization problem to changes in the auxiliary parameters. Foundational assumptions for HDSA require satisfaction of the optimality conditions which are not always practically feasible as a result of ill-posedness in the inverse problem. Here we introduce novel theoretical and computational approaches to justify and enable HDSA for ill-posed inverse problems by projecting the sensitivities on likelihood informed subspaces and defining a posteriori updates. Our proposed framework is demonstrated on a nonlinear multiphysics inverse problem motivated by estimation of spatially heterogeneous material properties in the presence of spatially distributed parametric modeling uncertainties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Quantum-Inspired Tensor Network Algorithm for Constrained Combinatorial Optimization Problems

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum-inspired tensor-network-based algorithm for general locally constrained combinatorial optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem, then encodes the constraints directly into a tensor network state and solves the optimal solution by evolving the system to the ground state of the Hamiltonian. We demonstrate our algorithm with the open-pit mining problem, which results in a quadratic asymptotic time complexity. Our numerical results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Convex Programs for Minimal-Area Problems

The minimal-area problem that defines string diagrams in closed string field theory asks for the metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. Here, we consider the analogous minimal-area problem for homology classes of curves and, with the aid of calibrations and the max flow-min cut theorem, formulate it as a local convex program. We derive an equivalent dual program involving maximization of a concave functional. These two programs give new insights into the form of the minimal-area metric and are amenable to numerical solution. We explain how the homology problem can be modified to provide the solution to the original homotopy problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Solving larger maximum clique problems using parallel quantum annealing

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach to the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A conservative discontinuous-Galerkin-in-time (DGiT) multirate time integration framework for interface-coupled problems with applications to solid–solid interaction and air–sea models

In this paper we extend the DGiT multirate framework, developed in Connors and Sockwell (2022) for scalar transmission problems, to a solid–solid interaction (SSI) problem involving two coupled elastic solids and a coupled air–sea model with the rotating, thermal shallow water equations. In so doing we aim to demonstrate the broad applicability of the mathematical theory and governing principles established in Connors and Sockwell (2022) to coupled problems characterized by subproblems evolving at different temporal scales. Further, multirate time integration algorithms employing different time steps, optimized for the dynamics of each subproblem, can significantly improve simulation efficiency for such coupled problems. However, development of multirate algorithms is a highly non-trivial task due to the coupling, which can impact accuracy, stability or other desired properties such as preservation of system invariants. DGiT provides a general template for multirate time integration that can achieve these properties. To elucidate the manner in which DGiT accomplishes this task, we fully detail each step in the application of the framework to the SSI and air–sea coupled problems. Numerical examples illustrate key properties of the resulting multirate schemes for both problems.

42 ENGINEERING↗
DOE OSTI2020

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that effectively leverage the complementary strengths of deterministic algorithms and QC techniques to overcome combinatorial complexity for solving large-scale mixed-integer programming problems. Four applications, namely the molecular conformation problem, job-shop scheduling problem, manufacturing cell formation problem, and the vehicle routing problem, are specifically addressed. Large-scale instances of these application problems across multiple scales ranging from molecular design to logistics optimization are computationally challenging for deterministic optimization algorithms on classical computers. To address the computational challenges, hybrid QC-based algorithms are proposed and extensive computational experimental results are presented to demonstrate their applicability and efficiency. The proposed QC-based solution strategies enjoy high computational efficiency in terms of solution quality and computation time, by utilizing the unique features of both classical and quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Deep learning of free boundary and Stefan problems

Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/DeepStefan.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Efficient hybrid explicit-implicit learning for multiscale problems

Splitting method is a powerful method to handle application problems by splitting physics, scales, domain, and so on. Many splitting algorithms have been designed for efficient temporal discretization. Here, in this paper, our goal is to use temporal splitting concepts in designing machine learning algorithms and, at the same time, help splitting algorithms by incorporating data and speeding them up. We propose a machine learning assisted splitting scheme which improves the efficiency of the scheme meanwhile preserves the accuracy. We consider a recently introduced multiscale splitting algorithms, where the multiscale problem is solved on a coarse grid. To approximate the dynamics, only a few degrees of freedom are solved implicitly, while others explicitly. This splitting concept allows identifying degrees of freedom that need implicit treatment. In this paper, we use this splitting concept in machine learning and propose several strategies. First, the implicit part of the solution can be learned as it is more difficult to solve, while the explicit part can be computed. This provides a speed-up and data incorporation for splitting approaches. Secondly, one can design a hybrid neural network architecture because handling explicit parts requires much fewer communications among neurons and can be done efficiently. Thirdly, one can solve the coarse grid component via PDEs or other approximation methods and construct simpler neural networks for the explicit part of the solutions. We discuss these options and implement one of them by interpreting it as a machine translation task. This interpretation of the splitting scheme successfully enables us using the Transformer since it can perform model reduction for multiple time series and learn the connection between them. We also find that the splitting scheme is a great platform to predict the coarse solution with insufficient information of the target model: the target problem is partially given and we need to solve it through a known problem which approximates the target. Our machine learning model can incorporate and encode the given information from two different problems and then solve the target problems. We conduct four numerical examples and the results show that our method is stable and accurate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Dimer piling problems and interacting field theory

The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We rediscover and explore an expression for the number of coverings of an arbitrary graph by arbitrary objects in terms of an interacting fermionic field theory first proposed by Samuel. Generalizations of the dimer tiling problem, which we call “dimer piling problems,” demand that each site be covered N times by indistinguishable dimers. Our field theory provides a solution of these problems in the large- N limit. We give a similar path integral representation for certain lattice coloring problems. Published by the American Physical Society 2024

Astronomy & Astrophysics↗