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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.

Mathematics↗
DOE OSTI2025

Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties With Deep Learning Multi‐Member and Stochastic Parameterizations

Abstract Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: (a) a single Deep Neural Network (DNN) with Monte Carlo Dropout; (b) a multi‐member parameterization; and (c) a Variational Encoder Decoder with latent space perturbation. We show that the multi‐member parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods (b) and (c) are advantageous compared to a dropout‐based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best‐performing multi‐member parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the superparameterization for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth‐like simulations but enables model stability over 5 months with our multi‐member parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the multi‐member parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of multi‐member machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

Behrens, Gunnar [Deutsches Zentrum für Luft‐ und R↗
DOE OSTI2025

Resilient Distributed Frequency Regulation of Renewable Generators under Communication Interruptions

Modern power systems (MPSs) face significant challenges due to the high penetration of renewable energy sources (RESs) and new types of loads such as electric vehicles (EVs). Traditional load frequency control (LFC) methods struggle with the intermittent, stochastic nature of RESs, the near-zero inertia of power-electronics-based generators, and the mobility of controllable loads and battery systems. This paper introduces a novel resilient distributed frequency regulation method to address these issues. The proposed method employs a state space model to represent the dynamic behavior of participating power sources while accounting for stochastic switching processes to model structural and parameter variations caused by disruptions such as generator connection/disconnection, communication interruptions, and physical faults. By integrating these dynamic and stochastic components, the method treats power grids as a comprehensive stochastic hybrid system. Our method enhances conventional frequency control by incorporating local stability control, neighborhood control decoupling, and coordination feedback. Theoretical analyses establish the stability, convergence, and resilience of the proposed method, and its effectiveness is validated through case studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Stochastic noise can be helpful for variational quantum algorithms

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms. Published by the American Physical Society 2025

Liu, Junyu↗
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 OSTI2024

Accurate numerical simulations of open quantum systems using spectral tensor trains

Decoherence between qubits is a major bottleneck in quantum computations. Decoherence results from intrinsic quantum and thermal fluctuations as well as noise in the external fields that perform the measurement and preparation processes. With prescribed colored noise spectra for intrinsic and extrinsic noise, we present a numerical method, Quantum Accelerated Stochastic Propagator Evaluation (Q-ASPEN), to solve the time-dependent noise-averaged reduced density matrix in the presence of intrinsic and extrinsic noise. Q-ASPEN is arbitrarily accurate and can be applied to provide estimates for the resources needed to error-correct quantum computations. We employ spectral tensor trains, which combine the advantages of tensor networks and pseudospectral methods, as a variational ansatz to the quantum relaxation problem and optimize the ansatz using methods typically used to train neural networks. Here, the spectral tensor trains in Q-ASPEN make accurate calculations with tens of quantum levels feasible. We present benchmarks for Q-ASPEN on the spin-boson model in the presence of intrinsic noise and on a quantum chain of up to 32 sites in the presence of extrinsic noise. In our benchmark, the memory cost of Q-ASPEN scales as a low-order polynomial in the size of the system once the number of system states surpasses the number of basis functions used in the spectral expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Denoising of imaginary time response functions with Hankel projections

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024

Yu, Yang (ORCID:0000000186178878)↗
DOE OSTI2026

Optical stochastic cooling at Fermilab’s IOTA ring

Stochastic cooling (SC) constitutes one of the greatest conceptual and technological achievements in particle beam cooling. Numerous SC systems have been built in the microwave regime and used to extend the science reach of accelerator facilities worldwide. The ability to sense and correct the particle ensemble using high-bandwidth feedback systems is at the core of the concept. Here, we describe the first realization of SC at optical frequencies and bandwidths. The demonstration was recently carried out at Fermilab’s integrable optics test accelerator (IOTA) storage ring using the transit-time method of optical stochastic cooling (OSC) and achieved an integrated system bandwidth of approximately 20 THz, which is more than 2000 times that of conventional SC systems. This demonstration establishes the foundation for more advanced OSC experiments with high-gain amplification, currently underway at Fermilab, and the eventual application of OSC to colliders and other accelerator facilities.

Jarvis, Jonathan D. [Fermilab]↗
DOE OSTI2025

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Applied Dynamical Systems↗
DOE OSTI2025

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Neutronics and Thermo-Fluids Simulation of Generic Pebble-Bed Fluoride-Salt-Cooled High-Temperature Reactor

The fluoride-salt-cooled high-temperature reactor (FHR) is one of the advanced reactors that has been attracting considerable interest from both the research community and the nuclear industry. To help facilitate the nuclear community's familiarity with the FHR, Kairos Power has developed a generic FHR (gFHR) benchmark. In the research performed here, this benchmark was used to assess innovative modeling methods that combine stochastic and deterministic computer codes to perform the design and analysis of the gFHR. Further, the Monte Carlo code Serpent 2 was used to generate few-group cross sections that were then used in the neutron diffusion and thermal-fluids code AGREE to perform full-core neutronics and thermal-fluids steady-state and transient core analysis. The Argonne National Laboratory code SAM was then used to model the gFHR system and to simulate the load-follow operation of the gFHR.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Optimizing stochastic algorithms for hadron correlation function computations in lattice QCD using a localized distillation basis

Distillation is a quark-smearing method for the construction of a broad class of hadron operators useful in lattice QCD computations and defined via a projection operator into a vector space of smooth gauge-covariant fields. A new orthonormal basis for this space is constructed which builds in locality. This basis is useful for the construction of stochastic methods to estimate the correlation functions computed in Monte Carlo calculations relevant for hadronic physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Data and code for Daily and Multi-Day Extreme Rainfall Analysis Under Future Climates Using Stochastic Storm Transposition and NEX-GDDP-CMIP6 Over CONUS

This data package provides inputs, codes, and outputs for a comprehensive analysis of projected changes in extreme precipitation across 10 regions of the continental United States, using 34 downscaled Earth System Models (ESMs) from the NASA Earth Exchange Global Daily Downscaled Projections, Coupled Model Intercomparison Project Phase 6 (NEX-GDDP-CMIP6) dataset. These models are part of the Coupled Model Intercomparison Project Phase 6 (CMIP6), a coordinated climate modeling framework widely used to assess climate change impacts. The analysis applies a stochastic storm transposition method to quantify changes in extreme rainfall under two Shared Socioeconomic Pathway (SSP) climate scenarios—SSP2-4.5 (moderate emissions) and SSP5-8.5 (high emissions)—compared to historical conditions (1995–2014 vs. 2081–2100). The dataset includes rainfall depth estimates for extreme events with return periods from 2 to 500 years across multiple storm durations (1, 3, and 5 days) for each of the 10 U.S. regions. Weighted ensemble statistics are derived from individual ESM performance against historical precipitation patterns, enabling robust uncertainty quantification through both sign-based and permutation-test-based model agreement assessments. Key analyses address: (1) relative changes in extreme precipitation for each climate scenario, (2) differences between SSP scenarios (SSP5-8.5 vs. SSP2-4.5), (3) contrasts between rare and frequent events, and (4) variations between multi-day and daily storm durations. The workflow produces ensemble statistics—median, 5th, 25th, 75th, and 95th percentiles—along with model agreement metrics that identify regions and event types with robust climate change signals. The dataset includes: processed rainfall depth outputs (netCDF format) from the RainyDay Python package, ESM weights from historical performance evaluation using DayMet observations, ensemble statistics across all storm dimensions, and figures summarizing key findings.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

GBOpt: Grain boundary structure optimization using Monte Carlo and evolutionary algorithms

Polycrystalline materials are made of many small crystals separated by grain boundaries (GBs), whose atomic structure strongly influences material properties. Because the structure of a GB determines its properties, the optimal structure must be known in order to determine those impacts. There are many ways of placing atoms in the GB region, but the optimal structure is defined as the one that gives the lowest value of a target property (typically energy). GB structure optimization has been successfully demonstrated using stochastic and evolutionary methods, but no reusable, community-maintained open-source workflow has been developed. GBOpt (Grain Boundary Optimization) is an open-source Python package that creates that workflow, where we have presently implemented two approaches: Markov Chain Monte Carlo, and genetic algorithm based on elite selection. We demonstrate this capability by successfully reproducing the known optimal structures of a specific GB in two materials, and point interested readers to the GitHub repository for additional examples, including optimization for different properties. Both of the implemented approaches recovered the known structures, with the genetic algorithm approach finding the optimal structure faster on average.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2025

Elucidation of Local Ordering and Atomic-Scale Structure in Polymer-Derived SiOC

Silicon oxycarbide (SiOC) is a versatile ceramic material with tunable microstructure and compositions that can be modulated through precursor chemistry and processing conditions. Though there are several noteworthy uses of SiOC across a range of application spaces, the difficulties in elucidating the short- to medium-range order within these materials have limited the maturation of strategies to precisely control SiC x O 4–x compositions for user-tailored applications. In this contribution, we implement a range of synchrotron scattering and spectroscopy methods coupled with stochastic modeling techniques to elucidate changes in local chemistry and structure associated with the pyrolysis of a commercially available SiOC polymer precursor. Stochastic modeling approaches provide valuable insights into decoupling local Si–O and Si–C environments while confirming predominate heterogeneous phases in materials. Using pyrolysis temperatures between 250 to 800 °C results in a heterogeneous material predominately composed of SiOC and amorphous SiO 2 domains. At 1100 °C, redistribution of Si–C pairs in the SiOC network and Si–O from the SiO 2 domains create a more ordered SiOC phase with local cubic SiC-like ordering. In addition, residual carbon leads to a detectable carbon phases at 1100 °C that persist at higher temperatures. These efforts address the difficulties of obtaining atomic-scale insights into the local structure and nanoscale heterogeneities in SiOC, providing pathways toward establishing structure–property relationships for future materials development.

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

Validation of the stochastic inversion algorithm for acoustic travel-time tomography: a large eddy simulation study

Acoustic tomography (AT) is explored as a remote sensing technique to obtain instantaneous snapshots of temperature and velocity fluctuations for wind energy applications. This study integrates Large Eddy Simulation (LES) with the Stochastic Inversion (SI) method to validate the algorithm’s capacity for accurate reconstruction of atmospheric fluctuations. The initial findings demonstrate the efficacy of the method in accurately capturing the predominant flow structures. Normalized L2 error evaluations further inform the algorithm’s precision, with errors accentuated in less sampled peripheral regions. The results underscore the method’s promise as a non-intrusive observational tool, with ongoing development poised to improve its precision and reliability.

17 WIND ENERGY↗
DOE OSTI2025

Critical fluid dynamics in two and three dimensions

We describe a numerical method for simulating stochastic fluid dynamics near a critical point in the Ising universality class. This theory is known as model H, and is expected to govern the nonequilibrium dynamics of quantum chromodynamics (QCD) near a possible critical endpoint of the phase transition between a hadron liquid and the quark-gluon plasma. The numerical algorithm is based on a Metropolis scheme, and automatically ensures that the distribution function of the hydrodynamic variables in equilibrium is independent of the transport coefficients and only governed by the microscopic free energy. We verify dynamic scaling near the critical point of a two and three-dimensional fluid and extract the associated critical exponent z. Here, we find z≃3 in three dimensions, and z≃2 for a two-dimensional fluid. In a finite system, we observe a crossover between the mean field value z=4 and the true critical exponent z≃3 (z≃2 in d=2). This crossover is governed by the values of the correlation length and the renormalized shear viscosity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗