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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Designing a drone delivery network with automated battery swapping machines

Drones are projected to alter last-mile delivery, but their short travel range is a concern. In this study, we propose a drone delivery network design using automated battery swapping machines (ABSMs) to extend ranges. The design minimizes the long-term delivery costs, including ABSM investment, drone ownership, and cost of the delivery time, and locates ABSMs to serve a set of customers. We build a mixed-integer nonlinear program that captures the nonlinear waiting time of drones at ABSMs. To solve the problem, we create an exact solution algorithm that finds the globally optimal solution using a derivative-supported cutting-plane method. To validate the applicability of our program, we conduct a case study on the Chicago Metropolitan area using cost data from leading ABSM manufacturer and geographical data from the planning and operations language for agent-based regional integrated simulation (more commonly known as POLARIS). A sensitivity analysis identifies that ABSM service times and costs are the key parameters impacting the long-term adoption of drone delivery.

25 ENERGY STORAGE↗
DOE OSTI2025

Scalable Algorithms for Inverse Problems With High-Dimensional Parameter Spaces

Inverse problems, which involve inferring unknown parameters from observed data, present significant computational challenges, especially in large-scale settings with high-dimensional unknown parameters and nonlinear relationships between the unknowns and observations. Bayesian inference provides an approach for addressing these problems, often relying on sequential sampling methods like Markov chain Monte Carlo (MCMC) to approximate the posterior distribution of the parameters. However, MCMC methods become computationally demanding as the dimensionality of the problem increases, particularly in large-scale systems where likelihood evaluations rely on solving partial differential equations (PDEs) on large spatial domains with finely resolved meshes. To overcome these limitations, recent advancements have focused on designing scalable computa tional techniques – for both PDE simulations and sampling strategies – to make Bayesian methods feasible for high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Probability of Initiation in Neutron Transport

We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed-point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.

42 ENGINEERING↗
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
DOE OSTI2021

Spatial Mode Correction of Single Photons Using Machine Learning

Abstract Spatial modes of light constitute valuable resources for a variety of quantum technologies ranging from quantum communication and quantum imaging to remote sensing. Nevertheless, their vulnerabilities to phase distortions, induced by random media, impose significant limitations on the realistic implementation of numerous quantum‐photonic technologies. Unfortunately, this problem is exacerbated at the single‐photon level. Over the last two decades, this challenging problem has been tackled through conventional schemes that utilize optical nonlinearities, quantum correlations, and adaptive optics. In this article, the self‐learning and self‐evolving features of artificial neural networks are exploited to correct the complex spatial profile of distorted Laguerre–Gaussian modes at the single‐photon level. Furthermore, the potential of this technique is used to improve the channel capacity of an optical communication protocol that relies on structured single photons. The results have important implications for real‐time turbulence correction of structured photons and single‐photon images.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A robust offering strategy for wind producers considering uncertainties of demand response and wind power

This paper proposes a risk-constrained decision-making approach for a wind power producer participating in the day-ahead market. In the developed model, a flexible demand response trading scheme between the wind power producer and different customers is employed. Through the proposed demand response mechanism, the wind power producer is able to trade demand response resource internally with different customers, and then trade energy externally with the market to increase the expected profit and the wind energy utilization. The uncertainties in the wind power and demand response are modeled by using the information gap decision theory approach from risk averse (robust) and risk-seeking (opportunistic) perspectives. The objective of the robust model is to maximize the robust level while satisfying the desired profit, whereas the opportunistic model aims to evaluate the possibility of achieving windfall profits with favorable uncertainties. The overall offering strategy problem is modeled as a bi-objective mixed integer nonlinear programming, which is linearized by proper techniques and solved efficiently by using the normal boundary intersection technique. In this work, simulation results show that utilizing demand response resource to mitigate wind power deviations can increase a wind power producer's profit and reduce potential risks. In addition, the results demonstrate that the proposed bi-objective optimization approach enables the wind power producer to select appropriate offering decisions with respect to uncertainties.

17 WIND ENERGY↗
DOE OSTI2026

Accelerating kinetic plasma simulations with machine-learning-generated initial conditions

Computational models of plasma technologies often solve for the system operating conditions by time-stepping an initial value problem to a quasi-steady solution. However, the strongly nonlinear and multi-timescale nature of plasma dynamics often necessitate millions, or even hundreds of millions, of steps to reach convergence, reducing the effectiveness of these simulations for computer-aided engineering. We consider acceleration of kinetic plasma simulations via data-driven machine-learning-generated initial conditions, which initialize the simulations close to their final quasi-steady-state, thereby reducing the number of steps to reach convergence. Three machine-learning models are developed to predict the density and ion kinetic profiles of capacitively coupled plasma discharges relevant to the microelectronics industry. The models are trained on kinetic simulations over a range of device operating frequencies and pressures. Best performance was observed when simulations were initialized with ion kinetic profiles generated by a convolutional neural network, reducing the mean number of steps to reach convergence by 17.1× when compared to initialization with a zero-dimensional global model. We also outline a workflow for continuous data-driven model improvement and simulation speedup, with the aim of generating sufficient data for full device digital twins.

Artificial neural networks↗
DOE OSTI2022

Quantum simulations of hydrodynamics via the Madelung transformation

Developing numerical methods to simulate efficiently nonlinear fluid dynamics on universal quantum computers is a challenging problem. In this paper, a generalization of the Madelung transform is defined to solve quantum relativistic charged fluid equations interacting with external electromagnetic forces via the Dirac equation. The Dirac equation is discretized into discrete-time quantum walks which can be efficiently implemented on universal quantum computers. A variant of this algorithm is proposed to implement simulations using current noisy intermediate scale quantum (NISQ) devices in the case of homogeneous external forces. High resolution (up to N=2 17 grid points) numerical simulations of relativistic and nonrelativistic hydrodynamical shocks on current IBM NISQs are performed with this algorithm. Here, this paper demonstrates that fluid dynamics can be simulated on NISQs, and opens the door to simulating other fluids, including plasmas, with more general quantum walks and quantum automata.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Tokamak disruption simulation

UT contribution in this Tokamak Disruption Simulation (TDS) is to develop a parallel high‐order hybridized Discontinuous Galerkin (HDG) methods for large‐s cale MHD simulations. The following are the major goals: 1) Construction of HDG methods for linearized MHD, 2) Rigorous analysis for the HDG formulations for linearized MHD, 3) 2D and 3D simulations to verify the convergent of the HDG methods for linearized MHD, 4) multigrid solvers/preconditioners for HDG formulations, 5) HDG for reconnection problems, 6) Divergence cleaning with HDG, 7) HDG formulations for nonlinear MHD, 8) Picard fixed point HDG approach, 9) IMEX HDG‐DG for nonlinear HDG; 10) parallel large‐scale HDG for linear and nonlinear MHD simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Soliton Generation in Negative Thermal Expansion Materials

Strain solitons have been observed statically in several 2D materials and dynamically in substrate materials using ultrafast laser pulses. The latter case relies on lattice relaxation in response to ultrafast heating in a light-absorbing transducer material, a process which is sensitive to the thermal expansion coefficient. Here we consider an unusual case where the sign of the thermal expansion coefficient is negative, a scenario which is experimentally feasible in light of rapid and recent advances in the discovery of negative thermal expansion materials. We present numerical solutions to a nonlinear differential equation which has been repeatedly demonstrated to quantitatively model experimental data and discuss the salient results using realistic parameters for material linear and nonlinear elasticity. The solitons that emerge from the initial value problem with negative and positive thermal expansion are qualitatively different in several ways. The new case of negative thermal expansion gives rise to a nearly-periodic soliton train with chirped profile and free of an isolated shock front. We suggest this unanticipated result may be realized experimentally and assess the potential for certain applications of this generic effect.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Observation of Joule–Thomson photon-gas expansion

In recent years, a self-consistent optical thermodynamic framework has emerged that offers a systematic methodology to understand, harness and exploit the complex collective dynamics of multimode nonlinear systems. These developments now allow consideration of a series of longstanding problems in optics, including the prospect of funnelling the entire power flowing in a multimode system into its ground state, for which no methodology currently exists. Here, we demonstrate an all-optical Joule-Thomson expansion process mediated by photon-photon interactions whereby the temperature of the optical gas drops abruptly to zero. Our experiments in various configurations of coupled multicore nonlinear waveguide arrangements illustrate how light undergoing expansion-induced cooling can be channelled from arbitrary input states into the fundamental mode with near-unity efficiency. We show that the stability of the post-expansion state is ensured through an irreversible process of energy conversion. The all-optical thermodynamic phenomena explored in this study may enable innovative techniques where various uncorrelated but identical sources are merged into a unified spatially coherent state, offering a route for direct beam combining.

Kirsch, Marco S. (ORCID:0000000342798228)↗
DOE OSTI2020

Data-Driven Operator Theoretic Methods for Global Phase Space Learning

In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant subsets of a phase space from the spectral properties of the associated Koopman operator constructed from time-series data. Moreover, in the case when the system evolution is known locally in various invariant subspaces, then a phase space stitching result is proposed that can be applied to identify a global Koopman operator. A biological system, bistable toggle switch and a second-order nonlinear system example are considered to illustrate the proposed results. The construction of this global Koopman operator is very helpful in experimental works as multiple experiments can't be run at the same time starting from several initial conditions.

Nandanoori, Sai Pushpak↗
DOE OSTI2021

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗
DOE OSTI2023

A solvable model of a nonlinear extension of quantum mechanics

We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. Here, we hope that this simple example will elucidate some of the issues of interpreting nonlinear generalization of quantum mechanics that have been put forth to resolve questions about quantum measurement theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Chapter Nine - Automated Optimal Control in Energy Systems: The Reinforcement Learning Approach

With the development of smart grid technologies an increasing number of new devices and participants have joined modern energy systems and are inevitably making them more complicated and interdependent than ever. Optimally controlling such a complex energy system and maintaining its operation in a high-efficient, secure, and resilient manner are challenging tasks to the system operators. Fortunately, the revolution in deep learning and artificial intelligence (AI), both from hardware and algorithms perspectives, has provided new ideas and solutions to many previously intractable problems. As a result, this advance in computer science also sparked great research interests in utilizing AI in solving engineering problems related to the modern energy systems. Among many AI techniques, deep reinforcement learning (DRL) has demonstrated great potential for solving sequential optimization problems, which are very common in the engineering domains. Its ability to handle nonlinearity and stochasticity in controlled systems has out-competed many traditional optimal control algorithms. Therefore in this chapter, we focus on the state-of-the-art of DRL concepts and related algorithms, compare their pros and cons with traditional optimal control approaches and discuss the typical workflow for leveraging RL in solving complex problems in modern energy systems.

artificial intelligence↗
DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Incorporation of market signals for the optimal design of post combustion carbon capture systems

Recent studies have shown that fossil generators equipped with post-combustion carbon capture (PCC) systems are needed to reduce the cost of deep decarbonization. Such generators need to be flexible and responsive to grid conditions, particularly in a high variable renewable energy (VRE) environment. In this work, we evaluate the net present value (NPV) of retrofitting an existing natural gas combined cycle (NGCC) unit with a flexible PCC system while incorporating market signals from a high VRE grid. We use our industrial partner’s NGCC configuration as representative of existing NGCC units and Svante’s rapid-temperature swing adsorption (TSA) for PCC. Because of its ability to rapidly startup/shutdown and ramp-up/ramp-down, the chosen capture technology is very attractive for load-following operations. For a given set of market signals, we formulate a two-stage stochastic multi-period optimization problem, under the price-taker assumption, to simultaneously optimize the design of the capture system and operation of the entire plant. Rigorous models for the NGCC unit, PCC system, and compression system are developed using commercial process simulators and validated with either plant or vendor data. For computational tractability, we develop surrogate/reduced-order models for use in the optimization problem. The surrogate model for the NGCC plant is constructed by linearizing the rigorous dynamic model at 75% load, while data-driven nonlinear surrogate models for the capture and compression systems are constructed using simulation data from the rigorous models. The optimization problem, formulated as a mixed integer bilinear program, is implemented in the IDAES® integrated platform and solved to global optimality using Gurobi 9.5. Using this formulation, we determine the profitability of retrofitting an existing NGCC unit with the chosen capture system for multiple regions in the U.S. under two scenarios with different carbon prices. Importantly, the results show that the optimal decision strongly depends on the region and on the carbon price, thereby demonstrating the importance of the inclusion of market signals in the design process.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗