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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗
DOE OSTI2025

Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.

Bounded domains↗
DOE OSTI2026

Identifying stochastic dynamics via finite expression methods

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty in generalizing beyond their training domain. Here, this paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems.

Complex dynamical systems↗
DOE OSTI2022

Mesh objective stochastic simulations of quasibrittle fracture

Continuum finite element (FE) modeling of damage and failure of quasibrittle structures suffers from the spurious mesh sensitivity due to strain localization. Here this issue has been addressed for deterministic analysis through the development of localization limiters. Here this study proposes a mechanism-based model to mitigate the mesh sensitivity in stochastic FE simulations of quasibrittle fracture. The interest is placed on the analysis of large-size structures, where the mesh size is conveniently chosen to be larger than the width of the fracture process zone as well as the correlation length of the random fields of constitutive properties. The present model is formulated within the framework of continuum damage mechanics. Two localization parameters are introduced to describe the evolution of the damage pattern of each finite element. These parameters are used to guide the energy regularization of the constitutive law, as well as to formulate the mesh-dependent probability distributions of constitutive properties. Depending on the prevailing damage pattern, different energy regularization schemes and mesh dependence of the probability distribution functions are used in the constitutive law. The model is applied to simulate the stochastic failure behavior of quasibrittle structures of different geometries featuring different failure processes including damage initiation, localization, and propagation. It is shown that using fixed probability distribution functions of constitutive properties could lead to strong mesh dependence of the prediction of the mean and variance of the structural load capacity. The probability distribution functions of constitutive properties must be linked to the damage pattern, which may evolve during the failure process. Such a mechanism-based modeling of the probability distributions of constitutive properties is essential for mitigating the spurious mesh sensitivity in stochastic FE analysis of quasibrittle fracture.

42 ENGINEERING↗
DOE OSTI2023

Energetic electron transport in magnetic fields with island chains and stochastic regions

This paper investigates energetic electron transport in magnetized toroidal plasmas with magnetic fields characterized by island chains and regions of stochastic field lines produced by coil perturbations. We report on experiments performed in the DIII-D tokamak, which utilize electron cyclotron heating and current drive pulses to ‘tag’ electron populations within different locations across the discharge. The cross-field transport of these populations is then inferred from electron cyclotron emission measurements and gamma emission signals from scintillator detectors. Two types of energetic particles are distinguished and discussed: non-relativistic suprathermal electrons and relativistic runaway electrons. The magnetic field topology in each discharge is reconstructed with field-line tracing codes, which are also used to determine the location and scale of magnetic islands and stochastic regions. Comparison of simulations and experiments suggests that suprathermal transport is suppressed when the tagging is performed at a smaller radial location than the location of the $q = 1$ island chain and enhanced otherwise. Here q is the safety factor. We further demonstrate that increasing the width of the stochastic region within the edge plasma yields enhancement of the suprathermal electron transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Tempering stochastic density functional theory

Here, we introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a "warm" component complemented by "colder" correction(s). Since the warm component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction in the statistical fluctuations and systematic deviation compared to sDFT for the same computational effort. We demonstrate the method's performance on large hydrogen-passivated silicon nanocrystals, finding a reduction in the systematic deviation in the energy by more than an order of magnitude, while the systematic deviation in the forces is also quenched. Similarly, the statistical fluctuations are reduced by factors of ≈4-5 for the total energy and ≈1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Stochastic Optimization to Find Optimum Beginning-of-Life Core Configuration of Stable Salt Reactor with Online Refueling

A stochastic optimization method has been developed to find an optimum equilibrium cycle core configuration of the waste-burning stable salt reactor, which is a fast-spectrum molten salt reactor with frequent online refueling. An optimum core configuration was determined with the goal of minimizing radial power peaking. Because of the vast number of potential candidate core configurations, stochastic optimization was applied based on simulated annealing and an additional acceleration method, which screened out unpromising core configurations. It has been demonstrated that the developed stochastic optimization method successfully finds the optimal core configuration regardless of the initial guess and outperforms the gradient descent approach. In addition, it has been observed that the use of a so-called out-in core configuration as the initial guess speeds up convergence of the iterative solution more than five times. Based on the searched optimum equilibrium cycle core configuration, new beginning-of-life (BOL) core configurations have been developed. In conclusion, the new BOL core configurations will be used in developing optimum refueling strategies.

Moltex static salt reactor↗
DOE OSTI2023

Bayesian filtering for model predictive control of stochastic gene expression in single cells

This study describes a method for controlling the production of protein in individual cells using stochastic models of gene expression. By combining modern microscopy platforms with optogenetic gene expression, experimentalists are able to accurately apply light to individual cells, which can induce protein production. Here we use a finite state projection based stochastic model of gene expression, along with Bayesian state estimation to control protein copy numbers within individual cells. We compare this method to previous methods that use population based approaches. We also demonstrate the ability of this control strategy to ameliorate discrepancies between the predictions of a deterministic model and stochastic switching system.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Demand Response Under Stochastic, Price-Dependent User Behavior

This letter focuses on price-based demand response (DR) implemented through dynamic adjustments of electricity prices. It extends existing DR models to a stochastic framework in which customer response is represented by price-dependent random variables, leveraging models and tools from the theory of stochastic optimization with decision-dependent distributions. The inherent epistemic uncertainty in the customers' responses renders open-loop, model-based DR strategies impractical. We propose a stochastic, feedback-based pricing strategy to compensate for estimation errors and uncertainty in customer response, establish theoretical results demonstrating the stability and near-optimality of the proposed approach, and validate its effectiveness through numerical simulations.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

Will Stochastic Devices Play Nice With Others in Neuromorphic Hardware?: There’s More to a Probabilistic System Than Noisy Devices

Achieving brain-like efficiency in computing requires a co-design between the development of neural algorithms, brain-inspired circuit design, and careful consideration of how to use emerging devices. The recognition that leveraging device-level noise as a source of controlled stochasticity represents an exciting prospect of achieving brain-like capabilities in probabilistic neural algorithms, but the reality of integrating stochastic devices with deterministic devices in an already-challenging neuromorphic circuit design process is formidable. Here, we explore how the brain combines different signaling modalities into its neural circuits as well as consider the implications of more tightly integrated stochastic, analog, and digital circuits. Further, by acknowledging that a fully CMOS implementation is the appropriate baseline, we conclude that if mixing modalities is going to be successful for neuromorphic computing, it will be critical that device choices consider strengths and limitations at the overall circuit level.

42 ENGINEERING↗
DOE OSTI2020

Scenario Creation and Power-Conditioning Strategies for Operating Power Grids with Two-Stage Stochastic Economic Dispatch

A significant difficulty associated with the use of stochastic programming to solve optimal power flow problems on a 5-minute timescale is the quality of renewable energy scenarios input by the user. This is especially true when considering power systems with high penetrations of renewable energy, e.g. wind power. This paper introduces the use of stochastic programming to solve the DC optimal power flow problem with scenarios drawn directly from high-fidelity data sets. Hence, the proposed method avoids the problem of lost physics by finding high-fidelity analogs that can describe future states of the system. Furthermore, this method can be simply extended to output multi-period scenarios to the stochastic program. We demonstrate the effectiveness of this technique by simulating dispatch operations on a synthetic test system over the course of a week.

94 GMLC - Grid Modernization Laboratory Consortium↗
DOE OSTI2025

Stochastic Model Predictive Control With Gaussian Wind Direction Preview for Wake Steering

This article addresses the problem of wake steering control for wind farms that explicitly consider the tradeoff between farm-level power generation and yaw duty cycle under variable and uncertain wind conditions. A novel stochastic model predictive control (MPC) algorithm is presented, which utilizes a stochastic model of the freestream wind field components in a receding horizon framework to compute optimal yaw set points that maximize the expected value of the farm power while constraining the yaw actuation. Different configurations of the algorithm are evaluated using a steady-state wind farm simulator. The proposed stochastic MPC algorithm can plan control actions over a future prediction horizon based on probabilistic estimates of the incoming wind magnitude and direction.

17 WIND ENERGY↗
DOE OSTI2021

Observability Analysis of a Power System Stochastic Dynamic Model Using a Derivative-Free Approach

Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. In this work, facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments

Here, we present a novel stochastic approach to binary optimization suited for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. This formulation (a) is generally applicable to binary optimization problems with soft constraints and is ideal for OED and sensor placement problems; (b) does not require differentiability of the original objective function (e.g., a utility function in OED applications) with respect to the design variable, and thus it enables direct employment of sparsity-enforcing penalty functions such as $\ell_0$, without needing to utilize a continuation procedure or apply a rounding technique; (c) exhibits much lower computational cost than traditional gradient-based relaxation approaches; and (d) can be applied to both linear and nonlinear OED problems with proper choice of the utility function. The proposed approach is analyzed from an optimization perspective with detailed convergence analysis of the optimization approach and is also analyzed from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Stochastic Continuous-time Flexibility Scheduling and Pricing in Wholesale Electricity Markets

Large-scale integration of intermittent renewable energy sources (RES) is calling for additional flexibility resources as well as more advanced modeling and optimization techniques to account for the increasing uncertainty and variability in power systems operation. As the RES integration gains momentum, the magnitude and frequency of their variations increase, which may trigger ramping scarcity events in real-time power systems operation. This necessitates revisiting the present definition of power systems flexibility and reserve services to reflect their robustness and adequacy towards sub-interval variations of the load and RES, as well as adjusting the operation models to accommodate the new reserve services. This project took a fundamental approach and aimed at developing continuous-time scheduling and pricing model that accurately models the continuous-time variations of load and RES and efficiently deploys the ramping capability of flexible resources to compensate the sources of variability and uncertainty in the market. In this regard, this project pursued the following goals: Developing stochastic multi-fidelity continuous-time optimization models for scheduling of energy storage (ES) systems and flexible loads in wholesale energy markets; Developing the theory and practices of continuous-time locational marginal pricing for valuating energy storage systems and flexible loads in wholesale energy markets; Developing function space solution approach to convert the proposed stochastic multi-fidelity continuous-time optimization models into tractable mixed-integer linear optimization models; and Defining flexibility reserve as a new type of reserve in markets that would enable ultimate participation of energy storage devices in provision of services to compensate the variability and uncertainty of RES in electricity markets. This project successfully completed all five major tasks defined in the SOPO, and produced 8 high-impact journal papers, 6 conference papers, 3 published U.S. patents, and one web-based software for continuous-time operation optimization of power systems. The application of the proposed flexibility reserve and the stochastic multi-fidelity continuous-time operation scheduling models would modify the forward commitment and schedule of generating units, ES devices and flexible loads, and would line up the resources in such a way that the composition of available resources is better prepared to respond to the sub-hourly variations of the load and renewable resources in real-time operation. Therefore, this project paves the way to sustainable, reliable, and economic integration of renewable energy resources in power system, supporting the progress towards reaching the national targets on energy independence. Even if the proposed models offers a radically different point of view as compared to existing models, it does not alter fundamentally the architecture of power systems operations, nor the complexity of the scheduling problem, so the integration of this project in power systems is extremely practical.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Statistical Learning for Nonlinear Model Reduction from Local Simulations of Stochastic and Particle- and Agent-Based Systems

Stochastic physical systems across the sciences that have very high-dimensional state spaces, with a large number of fast degrees of freedom that force direct simulators to proceed by integration steps that are orders of magnitude smaller than events of interests (e.g., particle collisions). Examples range from molecular motion to dynamics of large populations of cells. A grand challenge in the simulation and understanding of such systems is the systematic construction of accurate, interpretable, reduced models, enabling faster simulations, revealing fundamental properties of the dynamics, and predicting phenomena of interest that the original simulator could not reached with sufficient accuracy or within a given computational budget. In this projected we developed novel statistical estimation/machine learning techniques for analyzing and building empirical reduced models for important families of high-dimensional stochastic systems, in particular: - we developed techniques for estimating interaction kernels in interacting particle- and agent-based systems, which are ubiquitous in Physics, Biology and many other sciences, given observed trajectories of the system; - we developed techniques for nonlinear model reduction for high-dimensional stochastic systems that have a small number of unknown, nonlinear slow variables, and a large number of fast modes, that are possibly of large magnitude, given observed short trajectories of the system in the form of bursts of trajectories from different initial conditions; - we developed novel techniques for estimating linear dynamical systems on graphs when both the dynamics and the underlying graph are unknown, and we have a sparse set of space-time observations; - we considered the problem of estimating an unknown nonlinear observation function of a standard process (e.g. Brownian motion), so that we can recognized if an observed dynamics is "just" a nonlinear version of a known dynamics; we also developed benchmarks for learning algorithms aimed at learning and classifying diffusion processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

STOCHASTIC OPTIMIZATION FOR LONG TERM CAPITAL STRUCTURES, SYSTEMS, AND COMPONENTS REFURBISHMENT AND REPLACEMENT

As commercial nuclear power plants (NPPs) pursue extended plant operations in the form of Second License Renewals (SLRs), opportunities exist for these plants to provide capital investments to ensure long-term, safe, and economic performance. Several utilities have already announced their intention to pursue extended operations for one or more of their NPPs via SLR2. The goal of this research is to develop a riskinformed approach to evaluate and prioritize plant capital investments made in preparation for, and during the period of, extended plant operations to support decisions in NPP operations. In order to prioritize project selection via a riskinformed approach we developed a single decision-making tool that integrates safety/reliability, cost, and stochastic optimization models to provide users with data analysis capabilities to more cost effectively manage plant assets. Both stochastic analysis methods—such as Monte Carlo-based sampling strategies—and multi-stage stochastic optimization strategies are employed to provide priority lists to decisionmakers in support of risk-informed decisions. We applied the proposed method to a trial application of projected replacement/refurbishment expenditures for plant capital assets (i.e., Structures, Systems, and Components [SSCs]). The objective is to optimize the SSC replacement/refurbishment schedule in terms of economic constraints, data uncertainties, and SSC reliability data, as well to generate a priority list for maximizing returns on investment.

42 ENGINEERING↗
DOE OSTI2020

Scenario Creation and Power-Conditioning Strategies for Operating Power Grids with Two-Stage Stochastic Economic Dispatch: Preprint

A significant difficultly associated with the use of stochastic programming to solve optimal power flow problems on a 5-minute timescale is the quality of renewable energy scenarios input by the user. This is especially true when considering power systems with high penetrations of renewable energy, e.g. wind power. This paper introduces the use of stochastic programming to solve the DCOPF problem with scenarios drawn directly from high-fidelity data sets. Hence, the proposed method avoids the problem of lost physics by finding high-fidelity analogs that can describe future states of the system. Furthermore, this method can be simply extended to output multi-period scenarios to the stochastic program. We demonstrate the effectiveness of this technique on simulated dispatch operations of the RTS-GMLC over a week.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗