Search NASA⌕ Search

SEARCH · Search NASA

Results for “solve”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

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

An Online Approach to Solve the Dynamic Vehicle Routing Problem with Stochastic Trip Requests for Paratransit Services

Many transit agencies operating paratransit and microtransit services have to respond to trip requests that arrive in real-time, which entails solving hard combinatorial and sequential decision-making problems under uncertainty. To avoid decisions that lead to significant inefficiency in the long term, vehicles should be allocated to requests by optimizing a non-myopic utility function or by batching requests together and optimizing a myopic utility function. While the former approach is typically offline, the latter can be performed online. We point out two major issues with such approaches when applied to paratransit services in practice. First, it is difficult to batch paratransit requests together as they are temporally sparse. Second, the environment in which transit agencies operate changes dynamically (e.g., traffic conditions can change over time), causing the estimates that are learned offline to become stale. To address these challenges, we propose a fully online approach to solve the dynamic vehicle routing problem (DVRP) with time windows and stochastic trip requests that is robust to changing environmental dynamics by construction. We focus on scenarios where requests are relatively sparse—our problem is motivated by applications to paratransit services. We formulate DVRP as a Markov decision process and use Monte Carlo tree search to evaluate actions for any given state. Accounting for stochastic requests while optimizing a non-myopic utility function is computationally challenging; indeed, the action space for such a problem is intractably large in practice. To tackle the large action space, we leverage the structure of the problem to design heuristics that can sample promising actions for the tree search. Our experiments using real-world data from our partner agency show that the proposed approach outperforms existing state-of-the-art approaches both in terms of performance and robustness.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Solving Eco-Driving Problems Using Indirect Collocation Method and Smooth Representation

Here, we discuss the eco-driving problem, considering both electric and conventional powertrains, and presents a pathway to solving it numerically using an indirect collocation method. Despite the low-order system dynamics, the piecewise fuel/efficiency map, gear shifting, and real-world traffic/road situations bring system discontinuities/switchings and pure state constraints into the problem formulation, which make the problem highly nonlinear and nontrivial to solve. This letter introduces smooth approximations to convert the original problem to an unconstrained (and penalized) smooth boundary-value problem. This approach eliminates the discussion of the switching structure and leads to a lightweight Newton-method-based solution procedure.

42 ENGINEERING↗
DOE OSTI2021

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Deep Generative Models that Solve PDEs: Distributed Computing for Training Large Data-Free Models

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been recently reported that successfully solve PDEs, with examples including deep feed forward networks, generative networks, and deep encoder-decoder networks. However, practical adoption of these approaches is limited by the difficulty in training these models, especially to make predictions at large output resolutions (≥1024×1024). Here we report on a software framework for data parallel distributed deep learning that resolves the twin challenges of training these large SciML models - training in reasonable time as well as distributing the storage requirements. Our framework provides several out of the box functionality including (a) loss integrity independent of number of processes, (b) synchronized batch normalization, and (c) distributed higher-order optimization methods. We show excellent scalability of this framework on both cloud as well as HPC clusters, and report on the interplay between bandwidth, network topology and bare metal vs cloud. We deploy this approach to train generative models of sizes hitherto not possible, showing that neural PDE solvers can be viably trained for practical applications. We also demonstrate that distributed higher-order optimization methods are 2-3× faster than stochastic gradient-based methods and provide minimal convergence drift with higher batch-size.

PDEs↗
DOE OSTI2023

Fast Tuning-Free Distributed Algorithm for Solving the Network-Constrained Economic Dispatch

With the increasing penetration of distributed energy resources (DERs) and their participation in the electricity market, it becomes more desirable to apply distributed algorithms for resource allocation in order to address the resulting computational and communicational challenges. Most of the existing distributed algorithms for solving the network-constrained economic dispatch (NCED) problem require the tuning of certain auxiliary parameters. As a result, the robustness of these algorithms against the varieties in DERs is greatly undermined. In this paper, a new distributed algorithm, optimality condition consensus (OCC), is proposed to solve the NCED problem by using distributed power flow (DPF) and ratio consensus as fundamental tools. It inherits the advantages of existing distributed algorithms for the NCED problem but removes the need for parameter tuning to improve performance in practice. In conclusion, the effectiveness of the proposed distributed algorithm in terms of efficiency, scalability, and robustness is demonstrated through detailed case studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

hypredrive: high-level interface for solving linear systems with hypre

This software introduces a high-level interface designed to simplify solving linear systems using hypre, a renowned library for such computational challenges. It is crafted to be accessible and user-friendly, making the powerful capabilities of hypre available to a broader audience without requiring in-depth technical knowledge. The interface is characterized by its use of YAML for input, a format celebrated for its structured yet straightforward readability. This choice ensures that users can easily configure the software to meet their specific needs. Additionally, the software boasts an intuitive API that encapsulates hypre's functionalities, making it easier for users to interact with the process of solving linear systems. It is particularly beneficial for prototyping, offering a quick and efficient means to test various solver and preconditioner configurations. Furthermore, the software allows for the creation of an offline testing framework in which predefined linear systems are read from files and benchmarked with user-defined solution strategies. This makes it an invaluable tool for developers and researchers exploring and validating their computational models. Overall, the software serves as a bridge, bringing the advanced computational capabilities of hypre closer to users who may need more specialized technical expertise, thereby facilitating innovation and exploration in the field of numerical linear algebra.

Paludetto Magri, Victor↗
DOE OSTI2025

Ipopt Interface to Re::Solve Linear Solver

The software provides Ipopt optimization package an interface to the Re::Solve linear solver library. Re::Solve features GPU-resident direct and iterative linear solvers that could be used to accelerate optimization computations.

Alam, Maksudul [Oak Ridge National Laboratory (ORN↗
DOE OSTI2024

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries

Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1}$), where $d$ is the domain’s dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Finally, our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Solving multiphysics-based inverse problems with learned surrogates and constraints

Abstract Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO 2 plume predictions near, and far away, from the monitoring wells.

Yin, Ziyi (ORCID:0000000250248771)↗
DOE OSTI2025

Designing a Framework for Solving Multiobjective Simulation Optimization Problems

Multiobjective simulation optimization (MOSO) problems are optimization problems with multiple conflicting objectives, where evaluation of at least one of the objectives depends on a black-box numerical code or real-world experiment, which we refer to as a simulation. Whereas an extensive body of research is dedicated to developing new algorithms and methods for solving these and related problems, it is challenging and time-consuming to integrate these techniques into real-world production-ready solvers. This is partly because of the diversity and complexity of modern state-of-the-art MOSO algorithms and methods and partly because of the complexity and specificity of many real-world problems and their corresponding computing environments. The complexity of this problem is only compounded when introducing potentially complex and/or domain-specific surrogate-modeling techniques, problem formulations, design spaces, and data acquisition functions. Here, this paper carefully surveys the current state of the art in MOSO algorithms, techniques, and solvers, as well as problem types and computational environments where MOSO is commonly applied. We then present several key challenges in the design of a parallel multiobjective simulation optimization framework (ParMOO) and how they have been addressed. Finally, we provide two case studies demonstrating how customized ParMOO solvers can be quickly built and deployed to solve real-world MOSO problems.

engineering design optimization↗
DOE OSTI2023

Applying Physics-Informed Neural Networks to Solve Navier–Stokes Equations for Laminar Flow around a Particle

In recent years, Physics-Informed Neural Networks (PINNs) have drawn great interest among researchers as a tool to solve computational physics problems. Unlike conventional neural networks, which are black-box models that “blindly” establish a correlation between input and output variables using a large quantity of labeled data, PINNs directly embed physical laws (primarily partial differential equations) within the loss function of neural networks. By minimizing the loss function, this approach allows the output variables to automatically satisfy physical equations without the need for labeled data. The Navier–Stokes equation is one of the most classic governing equations in thermal fluid engineering. This study constructs a PINN to solve the Navier–Stokes equations for a 2D incompressible laminar flow problem. Flows passing around a 2D circular particle are chosen as the benchmark case, and an elliptical particle is also examined to enrich the research. The velocity and pressure fields are predicted by the PINNs, and the results are compared with those derived from Computational Fluid Dynamics (CFD). Additionally, the particle drag force coefficient is calculated to quantify the discrepancy in the results of the PINNs as compared to CFD outcomes. The drag coefficient maintained an error within 10% across all test scenarios.

Hu, Beichao (ORCID:0009000163215151)↗
DOE OSTI2021

Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most k nonzero elements, where k is relatively small compare to the dimension of the matrix to be partially diagonalized. Here, this type of problem arises in applications in which the desired eigenvector exhibits localization properties and in large-scale eigenvalue computations in which the amount of computational resource is limited. When the positions of these nonzero elements can be determined, we can obtain the k-sparse approximation to the original problem by computing eigenvalues of a k × k submatrix extracted from k rows and columns of the original matrix. We review a previously developed greedy algorithm for incrementally probing the positions of the nonzero elements in a k-sparse approximate eigenvector and show that the greedy algorithm can be improved by using an RL method to refine the selection of k rows and columns of the original matrix. We describe how to represent states, actions, rewards and policies in an RL algorithm designed to solve the k-sparse eigenvalue problem and demonstrate the effectiveness of the RL algorithm on two examples originating from quantum many-body physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

Trends in problem-solving research - Twelve recently described tasks.

Review of descriptions of the 12 problem-solving tasks developed since the last review (Ray, 1955) of this topic, indicating that the newer tasks are more sophisticated in design and provide for better experimental control than those used prior to 1953. Validity, reliability, sensitivity, trainability, problem structure, and problem difficulty are discussed as criteria for the selection of tasks to be used in studies of skilled problem-solving performance.

Coates, G. D.↗
NASA NTRS1972

Robot, computer problem solving system

The development of a computer problem solving system is reported that considers physical problems faced by an artificial robot moving around in a complex environment. Fundamental interaction constraints with a real environment are simulated for the robot by visual scan and creation of an internal environmental model. The programming system used in constructing the problem solving system for the simulated robot and its simulated world environment is outlined together with the task that the system is capable of performing. A very general framework for understanding the relationship between an observed behavior and an adequate description of that behavior is included.

Becker, J. D.↗
NASA NTRS1975

A numerical scheme to solve unstable boundary value problems

A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.

Kalnay Derivas, E.↗
NASA NTRS1976

A new method for solving problems of sound radiation from a duct for the case of low Mach number

A method for rapidly solving duct end-plane impedance problems is presented which is based on deriving a form of the Helmholtz integral formula expressing the normal derivative of the acoustic pressure at a boundary point. A set of integral expressions is obtained by satisfying the existing boundary conditions and then solved using a general collocation method. The results obtained for the Levine-Schwinger (1948) problem agree well with the exact values. In the case of a duct flow having a temperature mismatch with the surroundings, the results show an increase in the magnitude of the reflection coefficient for the case of a cold core, and a decrease in its value for the case of a hot core, as compared with the case of exhaust into a uniform medium. A phase change of between pi/2 and pi is nearly always achieved, which indicates the tendency towards maintaining a constant pressure at the exit plane. The method can easily be extended to arbitrary duct shapes as long as they are axisymmetric.

Wahbah, M. M.↗