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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

General algorithm for characterization of donor-acceptor pair recombination processes in solid-state materials

Radiative recombination processes can occur in solid-state systems through the pairing of donor and acceptor defects of the lattice. Recently, donor-acceptor pairs (DAP) have been proposed as promising candidates for quantum applications, and their signature has been observed in emerging low-dimensional materials. Therefore, the identification of such processes is gaining interest and requires methods to efficiently and reliably characterize them. Here, we introduce a general algorithm to identify DAP processes starting from the experimental photoluminescence (PL) emission spectrum and basic material parameters, including the lattice structure and dielectric constant. The algorithm recognizes possible DAP transitions from the emission pattern in the spectrum and returns the characteristic energy of the DAP transition and the separation between the donor and acceptor sites. By testing the algorithm on the photoluminescence spectrum of hexagonal boron nitride (hBN), we show that our method is robust against experimental errors and adds new capabilities to the investigation toolbox of semiconductors and their optical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Black Box Equations of State: Creating Semi-analytic Solutions to the Noh Problem and Verifying Equation of State Interfaces

The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

NUTRON NESHAPs Dashboard

My project aims to enhance the Nuclear Material Tracking Application (NUTRON) software by integrating a tool for the National Emission Standards for Hazardous Air Pollutants (NESHAP) emissions calculations and presenting this data on a dashboard. Inefficiencies in the current NESHAP calculation process were addressed, which will result in more timely regulatory compliance efforts. Key improvements include revising the transfer request system, incorporating effective dose calculations, and developing a data visualization dashboard into NUTRON. The project involved creating a wireframe, preparing an Engineering Calculations and Analysis Report (ECAR), stakeholder meetings, and providing supplemental documentation. Key findings indicate that the proposed modifications will streamline the NESHAP calculation process, reduce human error, and provide REC personnel with accurate and timely data for material use determinations and dose estimations. Future work focuses on completing the NUTRON modifications and fully integrating the new features, ensuring a more efficient and reliable system for tracking and reporting nuclear material transfers.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

Manufactured solutions for an electromagnetic slot model

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. Finally, we demonstrate the effectiveness of these approaches for a variety of cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise

Here, we present a family of local quantum channels whose steady-states exhibit stable mixed-state symmetry-protected topological (SPT) order. Motivated by recent experimental progress on "erasure conversion" techniques that allow one to identify ($\textit{herald}$) decoherence processes, we consider open systems with biased erasure noise, which leads to strongly symmetric heralded errors. We utilize this heralding to construct a local correction protocol that effectively confines errors into short-ranged pairs in the steady-state. Using a combination of numerical simulations and mean-field analysis, we show that our protocol stabilizes SPT order against a sufficiently low rate of decoherence. As the rate of heralded noise increases, SPT order is eventually lost through a directed percolation transition. We further find that while introducing unheralded errors destroys SPT order in the limit of long length- and time-scales, the correction protocol is sufficient for ensuring that local SPT order persists, with a correlation length that diverges as $\xi \sim (1-f_e)^{-1/2}$, where $f_e$ is the fraction of errors that are heralded.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Scalable quantum computational science: A perspective from block-encodings and polynomial transformations

Significant developments made in quantum hardware and error correction recently have been driving quantum computing toward practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented, including the construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this perspective serves as a gentle introduction to state-of-the-art quantum algorithms for the computational science community and inspires future development of scalable quantum computational science methodologies that bridge theory and practice.

Bayesian inference↗
DOE OSTI2025

Increased Ly α Opacity in White Dwarf Photospheres from Transient H − Resonances

The structure and emergent flux of hydrogen atmosphere white dwarfs depend on the opacity of the Lyα and Lyβ spectral lines. The opacity here is set by the strength and broadening of these lines; the latter is dictated by the far line wing, which is in the “quasi-static” limit of electron broadening, placing it in the incomplete collision regime, and describes the transient parts of electron and ion collisions. These transient stages of the collision form resonances: In the case of ions, they manifest as molecular resonances, while for electrons they are H − resonances, both of which can only be captured quantum-mechanically. Quantum-mechanical calculations have historically preserved only a handful of broadening terms that are most important near the center of the line. However, in the wings of the line, the previously neglected terms that describe the transient stages of the collision need to be included. This requirement arises because, in the line wings, the broadening from the 1s ground state, which is generally assumed to be extremely small compared to the broadening of the upper state, is no longer negligible within a quantum-mechanical model that takes into account exchange interactions. The inclusion of all the transient terms results in asymmetries and extra broadening. The increased broadening of Lyα increases the opacity at the energy where most of the flux leaves the star. The broader Lyα lines also impact the visible flux, raising it by an amount that exceeds previously estimated errors.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Train small, model big: Scalable physics simulators via reduced order modeling and domain decomposition

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. Here this method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ~1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Dissipation Scaled Internal Wave Drag in a Global Heterogeneously Coupled Internal/External Mode Total Water Level Model

This study showcases a global, heterogeneously coupled total water level system wherein salinity and temperature outputs from a coarser-resolution (~12 km) ocean general circulation model are used to calculate density-driven terms within a global, higher-resolution (~2.5 km) depth-averaged total water level model. We demonstrate that the inclusion of baroclinic forcing in the barotropic model requires modification of the internal wave drag term to prevent excess degradation of tidal results compared to the barotropic model. By scaling the internal tide dissipation by an easy to calculate dissipation ratio, the resulting heterogeneously coupled model has complex root mean square errors (RMSE) of 2.27 cm in the deep ocean and 12.16 cm in shallow waters for the M 2 tidal constituent. While this represents a 10%–20% deterioration as compared to the barotropic model, the improvements in total water level prediction more than offset this degradation. Global median RMSE compared to observations of total water levels, 30-day sea levels, and non-tidal residuals improve by 1.86 (18.5%), 2.55 (42.5%), and 0.36 (5.3%) cm respectively. The drastic improvement in model performance highlights the importance of including density-driven effects within global hydrodynamic models and will help to improve the results of both hindcasts and forecasts in modeling extreme and nuisance flooding. With only an 11% increase in model run time compared to the fully barotropic total water level model, this approach paves the way for high resolution coastal water level and flood models to be used alongside climate models, improving operational forecasting of total water levels.

Blakely, Coleman Peter [University of Notre Dame, ↗
DOE OSTI2026

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗
DOE OSTI2024

Dynamic Modeling of Near Isothermal Compressor for Transcritical Carbon Dioxide Cycle

Compressors are the major energy consumption components in vapor compression systems, drawing much research effort in reducing carbon emissions. The isothermal compressor integrates the compressor chamber and gas cooler to achieve near isothermal compression, reaching up to 30% energy reduction compared to the traditional isentropic compression work. This paper presents a detailed isothermal compressor model combined with a generalized liquid piston model to account for the carbon dioxide (CO2) isothermal compression process. The model is established based on MATLAB environment. The model uses the real experimental data as boundary conditions and initial settings, which also considers the CO2 solubility in liquid piston (mineral oil) for designing, optimizing and customizing the compression chambers. The validation was carried out with experimental data using a prototype with 3.5 kW capacity. The results have demonstrated the accuracy of the dynamic model (6.2% relative error for chamber pressure and 0.5 K deviation for chamber temperature), which provide a guideline for designing and customizing the isothermal compression cycle.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Power generation forecasting for solar plants based on Dynamic Bayesian networks by fusing multi-source information

A Dynamic Bayesian network (DBN) model for solar power generation forecasting in solar plants is proposed in this paper. The key idea is to fuse sensor data, operational indicators, meteorological data, lagged output power information, and model errors for more accurate short-term (e.g., hours) and mid-term (e.g., days to weeks) power generation forecasting. The proposed DBN augments automated data-driven structure learning with expert knowledge encoding using continuous and categorical data given constraints to represent causal relationships within a solar inverter system. Additionally, an error compensation mechanism is proposed to capture temporal fluctuation. The effectiveness of the DBN on solar power generation forecasting was evaluated by rolling window analysis with one-year testing data collected from a local solar plant. The proposed DBN is compared with four state-of-art methods including support-vector regression (SVR), k-nearest neighbors (kNN), artificial neural network (ANN), and long short-term memory (LSTM) models. The result show that the proposed DBN achieves better accuracy in general, and it is not as data-hungry as some neural network-based models. The proposed DBN is also shown to have robust and consistent forecasting power with different forecasting horizons. The accuracy is 92% - 95% from one hour to one week ahead forecasting.

14 SOLAR ENERGY↗
DOE OSTI2026

Transient Multiphysics Simulations with Pin Power Reconstruction in the Griffin Reactor Physics Code

This work introduces the pin power reconstruction capability available in the Griffin reactor physics code. This capability is implemented in an unstructured mesh framework, and the methods introduced are applied to the 2D SIMBA reactor core, which has assemblies and pins arranged in a hexagonal lattice. Since this reactor has a non-Cartesian geometry and also operates in the thermal spectrum, a general approach to pin power reconstruction is adopted, where SPH-based equivalence is leveraged to preserve assembly-wise reaction rates, while computing full-core form functions to preserve pin-wise fission production rates within the fuel pins of the reactor core. In a 2D microreactor benchmark problem, this pin power reconstruction approach was shown to reproduce pin powers compared to the Serpent2 Monte Carlo code for fixed temperature conditions and control drum rotation angles, yielding a core-wide RMS error level of 0.6\% and a maximum absolute pin error of 2.3\%. In addition, a tabulated library of multigroup cross sections, SPH factors, and form functions was generated to demonstrate the applicability of pin power reconstruction to a thermal feedback problem. Finally, a control drum transient was successfully simulated, showcasing the application of pin power reconstruction in a transient multiphysics feedback problem.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Polynomial Scaling Localized Active Space Unitary Selective Coupled Cluster Singles and Doubles

We present a polynomial-scaling algorithm for the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. In this approach, cluster excitations are selected based on a threshold ϵ determined by the absolute gradients of the LAS-UCCSD energy with respect to cluster amplitudes. Using the generalized Wick’s theorem for multireference wave functions, we derive the gradient expression as a polynomial function of one-, two-, and three-body reduced density matrices and 1- and 2-electron integrals, valid for any multireference wave function. The resulting gradient implementation exhibits a memory scaling of 𝒪(N 6 ), with N spin orbitals in the combined active space of all fragments. The variational quantum eigensolver is used to optimize the selected cluster excitations on a quantum simulator. Furthermore, by plotting the energy error, defined as the difference between the LAS-USCCSD and corresponding CASCI energies, against the inverse cluster amplitude selection threshold (ϵ –1 ) for polyene chains containing 2 to 5 π-bond units, we establish a relationship between the energy error and the threshold. To further validate the accuracy of LAS-USCCSD, we computed the cis–trans isomerization energy of stilbene (a 20-qubit system) and the magnetic coupling constant of the tris-hydroxo-bridged chromium dimer [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ (evaluated as both 12- and 20-qubit systems) using the Qiskit-Qulacs simulator. Assessing such examples is important to determine the practical feasibility of quantum simulations for chemically realistic systems. Toward this goal, with the LAS-USCCSD algorithm we estimated the quantum resources required for simulating an active space of (30e,22o) in [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ , a size that remains beyond the reach of current quantum simulators for accurate treatment.

Algorithms↗
DOE OSTI2024

Emergence of Microphysical Bulk Viscosity in Binary Neutron Star Postmerger Dynamics

Abstract In nuclear matter in isolated neutron stars, the flavor content (e.g., proton fraction) is subject to weak interactions, establishing flavor ( β -)equilibrium. However, there can be deviations from this equilibrium during the merger of two neutron stars. We study the resulting out-of-equilibrium dynamics during the collision by incorporating direct and modified Urca processes (in the neutrino-transparent regime) into general-relativistic hydrodynamics simulations with a simplified neutrino transport scheme. We demonstrate how weak-interaction-driven bulk viscosity in postmerger simulations can emerge and assess the bulk viscous dynamics of the resulting flow. We further place limits on the impact of the postmerger gravitational-wave strain. Our results show that weak-interaction-driven bulk viscosity can potentially lead to a phase shift of the postmerger gravitational-wave spectrum, although the effect is currently on the same level as the numerical errors of our simulation.

Astronomy & Astrophysics↗
DOE OSTI2024

EPCAPE-PT-LANL Measurements: Single Particle Soot Photometer

Coastal cities offer a unique environment for studying aerosol-cloud interactions and the effects of urban emissions on cloud properties. As part of the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE), the Partitioning Thrust by Los Alamos National Laboratory (EPCAPE-PT-LANL) was conducted. Our campaign focused on measuring the optical and chemical properties of aerosols and their interactions within marine stratocumulus clouds in La Jolla, California. EPCAPE-PT-LANL enhances the primary goals of EPCAPE through innovative observations of vapor-phase transitions between aerosols and cloud droplets, the impact of black carbon on aerosol-cloud dynamics, and the effects of cloud processing on aerosol optical properties. Instrument: Single Particle Soot Photometer (Droplet Measurements Technology) Data Notes: Contact us if you want additional data products from this instrument. Reported data is the black carbon (rBC) number and mass concentration with diagnostic flags. The SP2 measures incandescence from particles that is induced with a 1064 Nd-YAG laser. Particles that absorb the laser energy and then emit radiation is assumed to contain black carbon. The amount of intensity of radiation is related to the mass of absorbing material in the particle. Here, we calibrate the incandescence intensity to size selected Regal Black (Cabot) nebulized from solution. Data provided for the EPCAPE campaign used the combined broadband high-gain + low-gain channels (BHBL). Each channel has a lower threshold of detection equivalent to 2-s of the respective channel noise. Thresholding has been applied to select between the high-gain and low-gain channels. The detection limit is 80-540 nm (Deq) or 0.36- 55 fg. It is assumed that rBC is the only aerosol type that is in significant concentration in the sampled atmosphere that absorbs the laser energy. Particle data are integrated over 10 second windows to calculate a rBC number and mass concentration. QC/QA: • Diagnostic flags that impacted measured concentration: - Sample, Sheath, and Purge Flow Rates: Despite observing fluctuations in all flows, the rBC detection and mass quantification are generally observed to be stable, although large changes in sample flow rate did impact detection efficiency. A flag was implemented for sample flow deviations >12 cm3/min from the set point averaged over 30 seconds - Laser Power: Detection efficiency decreases with laser power and deviations in laser power also affect mass quantification. Flag for laser power is set for deviations in laser current from the set value >5 mA. - Primary Detector Threshold: Primary thresholding is the signal value which determines whether a “particle” is recorded. Thresholding errors occur when the threshold value is too HIGH and real particles are ignored. • Several periods without data: - 16-18 Nov: Ultra Zero Air generator failure, flows deviated significantly from set points. rBC # conc recovered but questionable. - 20-21 Nov: Offline for calibrations for several hours each day. - 25-27 Nov: Data is missing. - 30 Nov: Power outage 3 Dec: SP2 hard-drive full. - 3 Dec: Power Outage Header: - BHBL_NumbConc[#/cc]: Refers to the number concentration of refractory black carbon (rBC) measured from combined broadband high-gain and low-gain channels, expressed in particles per cubic centimeter. - BHBL_BCMass_Conc[ug/m3]: Refers to the mass concentration of refractory black carbon (rBC) measured from combined broadband high-gain and low-gain channels, expressed in micrograms per cubic meter. - NoData_Flag[bool]: A boolean flag that indicates whether no data was recorded during a measurement. - NoBC_Flag[bool]: A boolean flag indicating whether no black carbon particles were recorded during the measurement. - Laser_Flag[bool]: A boolean flag indicating deviations in laser current during the measurement. - SampleFlow_Flag[bool]: A boolean flag indicating deviations from the set sample flow rate during the measurement. - PrimThresh_Flag[bool]: A boolean flag indicating deviations from the set primary threshold during the measurement, potentially ignoring real particles. - Manual_Flag[bool]: A boolean flag indicating manual intervention or adjustments during the measurement. - CVI_Flag[bool]: A boolean flag indicating whether the Counterflow Virtual Impactor (CVI) was active or inactive during the measurement.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Bridging the time scale in exascale computing of chemical systems (Final Technical Report)

This report summarizes the work carried out with support of the United States Department of Energy under Award DE-SC0019441. The theme of this project was to develop and apply methods that allowed for the acceleration of atomistic calculations, particularly in challenging areas such as multiphase systems, electrified interfaces, uncertainty estimation, and applications requiring chemical accuracy, which tend to be applications where simulation time is severely bottlenecked by the computational time requirements. Much of the focus was on the application of emerging machine-learning methodologies, although a wide range of methodologies were employed. This report has two major sections. The first focuses on the methodological advances themselves. Within this part, we report a number of major advances, a few examples of which are described here. We report the first machine-learning scheme for the acceleration of electronically grand-canonical calculations (that is, those applicable to electrochemistry). We report new methods of performing transfer learning, in which physics-based priors can be used to provide predictions, often with uncertainty estimates, of images well outside of training sets; we also offer ways to fine-tune these transfer-learning models. We provide a new systematic means to generate and apply minimal training data sets to very large (10,000’s of atoms) systems, with only small training sets appropriate for electronic structure. We developed new methodologies to integrate surface vibrations into surface adsorption calculations. We made advances to the applicability of diffusion Monte Carlo methods to allow (learned) force prediction, finite-size error correction, and force-free means of searching for transition states. We integrated machine-learned atomistic predictions into mechanism generation codes. Additionally, we released new software including AmpTorch, a modernized version of our original atomistic machine-learning code Amp. The second part of this report focuses on the scientific applications that accompanied, and were often enabled by, the methodological advances described earlier. A few examples follow, but full details are in the individual chapters of the report. For example, we developed a general theory of phonon-induced friction on molecular adsorbates. We showed fundamentally how solvent influences the adsorption and desorption process and how it differs from the processes typically involved at the solid–gas interface, making aqueous-phase and electrocatalysis different from traditional thermocatalysis. We examined how metal–insulator and magnetic transitions can be probed, and accelerated exciton dynamics via Frenkel Hamiltonian parameters. We showed that the nearsighted force-training approach, developed within this project, can predict both the stability and reactivity of large nanoparticles, and can also lead to insights on catalyst coverage on binding energies and entropies. These applied studies, which generally integrated with our method development, allowed us to push forward the theoretical understanding of several reaction classes.

08 HYDROGEN↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗