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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

QCD evolution of entanglement entropy

Entanglement entropy has emerged as a novel tool for probing nonperturbative quantum chromodynamics (QCD) phenomena, such as color confinement in protons. While recent studies have demonstrated its significant capability in describing hadron production in deep inelastic scatterings, the QCD evolution of entanglement entropy remains unexplored. Here, in this work, we investigate the differential rapidity-dependent entanglement entropy within the proton and its connection to final-state hadrons, aiming to elucidate its QCD evolution. Our analysis reveals a strong agreement between the rapidity dependence of von Neumann entropy, obtained from QCD evolution equations, and the corresponding experimental data on hadron entropy. These findings provide compelling evidence for the emergence of a maximally entangled state, offering new insights into the nonperturbative structure of protons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Decoding Gas Evolution Pathways and Interfacial Chemistry in Layered Oxide Cathodes for Safer Sodium‐Ion Batteries

Sodium-ion batteries (SIBs) are attractive for the low cost and abundance of sodium. Yet, gas evolution—a critical challenge in SIBs—remains underexplored. Here, online electrochemical mass spectrometry is used to probe gas evolution in layered oxide cathodes with various compositions, cutoff voltages, dopants, and particle morphologies. Compared to LiNiO 2 (LNO), NaNiO 2 releases more gas, even at lower states of charge, due to the higher covalency of Ni─O bond caused by the more ionic Na─O bond through the inductive effect. Among Co, Mn, Al, and Mg, Mn and Mg doping suppress gas release most effectively by enhancing the metal-oxygen bond strength. NaNi 1/3 Fe 1/3 Mn 1/3 O 2 (NFM) cathodes synthesized via coprecipitation (CP-NFM) and solid-state routes exhibit distinct particle morphologies; CP-NFM exhibits more gas evolution, yet secondary particle morphology helps reduce it through differential cathode-electrolyte reactivity between inner and outer primary particles. Among Li, Ti, Mg, and Cu doping in NFM, Li has the largest effect, reducing gas levels comparable to LNO. Nuclear magnetic resonance and X-ray photoelectron spectroscopies reveal that electrolyte solvent decomposition mainly produces organic-rich cathode-electrolyte interphase (CEI) rather than soluble species. NaPF 6 salt further exacerbates cathode-electrolyte reactions, forming surface Na 2 O species. The findings provide actionable guidance for designing safer, durable SIBs.

25 ENERGY STORAGE↗
DOE OSTI2025

The Cosmic Evolution of C IV Absorbers at 1.4 < z < 4.5: Insights from 100,000 Systems in DESI Quasars

We present the largest catalog to date of triply ionized carbon (C IV ) absorbers detected in quasar spectra from the Dark Energy Spectroscopic Instrument. Using an automated matched-kernel convolution method with adaptive signal-to-noise thresholds, we identify 101,487 C IV systems in the redshift range 1.4 < z < 4.5 from 300,637 quasar spectra. Completeness is estimated via Monte Carlo simulations, and the catalog is 50% complete at EW C IV ≥ 0.4 Å. The differential equivalent width frequency distribution declines exponentially and shows weak redshift evolution. The absorber incidence per unit comoving path increases by a factor of 2–5 from z ≈ 4.5 to z ≈ 1.4, with stronger redshift evolution for strong systems. Using column densities derived from the apparent optical depth method, we constrain the cosmic mass density of C IV , Ω C IV , which increases by a factor of ∼3.8 from (0.82 ± 0.05) × 10 −8 at z ≈ 4.5 to (3.16 ± 0.2) × 10 −8 at z ≈ 1.4. From Ω C IV , we estimate a lower limit on intergalactic medium metallicity ${\mathrm{log}}({Z}_{{\rm{IGM}}}/{Z}_{\odot })\gtrsim -3.25$ at z ∼ 2.3, with a smooth decline at higher redshifts. These trends trace the cosmic star formation history and He II photoheating rate, suggesting a link between C IV enrichment, star formation, and UV background over ∼3 Gyr. The catalog also provides a critical resource for future studies connecting circumgalactic metals to galaxy evolution, especially near cosmic noon.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Preliminary study of auto-differentiation algorithm in beam dynamics with stochastic process

Modern particle accelerator optimization requires sophisticated computational methods to address the inherently stochastic nature of beam dynamics. This research develops a framework applying AD to SDEs that specifically addresses beam dynamics challenges in particle accelerators, focusing on accurately modeling and optimizing beam behavior in regimes dominated by stochastic processes. By incorporating key physical phenomena such as synchrotron radiation, wakefield effects, and quantum excitation, the framework aims to provide auto differentiation on the figure of merit of the phase space evolution and beam dynamics. The methodology will enable effective optimization method in a dynamic system with stochastic process.

Accelerator Physics↗
DOE OSTI2024

Swift

Swift is a fast Fourier transform based spectral solver based on the MOOSE framework. It supports GPU accelerated semi-implicit solves of partial differential equations, such as those used for phase field mesoscale microstructure evolution.

Schwen, Daniel [Idaho National Laboratory (INL), I↗
NASA NTRS2026

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy↗
DOE OSTI2026

Thermal cycling-driven microstructural changes of eutectic Al–Si phase change materials in SS304 containers revealed by multi-modal imaging

Aluminum-based Al–Si alloys are widely used as phase change materials (PCMs) in thermal energy storage (TES) systems owing to their high volumetric latent heat and superior thermal conductivity. However, their long-term reliability is limited by degradation processes that remain insufficiently understood. In this work, we employ a multimodal, correlative characterization framework to systematically resolve the degradation behavior of eutectic Al–Si PCMs in contact with SS304 containers under repeated thermal cycling. By integrating high-resolution electron microscopy, three-dimensional X-ray fluorescence (3D XRF) imaging, and differential scanning calorimetry (DSC), we directly link spatially resolved compositional and microstructural evolution to changes in thermophysical properties. The correlative analysis reveals that elemental leaching of Fe, Cr, and Ni from the stainless-steel container into the PCM drives the formation of intermetallic compounds (IMCs) both at the interface and within the bulk PCM, leading to pronounced compositional heterogeneity. These interfacial reactions and diffusion-induced transformations progressively destabilize the Al–Si eutectic, reducing the effective phase-transforming fraction. Consistent with these observations, DSC measurements show a decrease in melting temperature and latent heat of fusion with thermal cycling. These results underscore the critical influence of interfacial reactions and material compatibility on the stability, durability, and overall performance of Al–Si-based TES systems.

25 ENERGY STORAGE↗
DOE OSTI2025

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗
DOE OSTI2026

Time at Temperature Experiments on Neutron Irradiated Zircaloy-2 using Conventional & Flash DSC

Dryout events in Boiling Water Reactors (BWRs) are currently treated by NRC regulations as automatic disqualification for continued fuel rod operation, even though this criterion does not account for the rate or duration of power increases, associated changes in material behavior, or the possibility of rewetting. Operational history from Anticipated Operational Occurrences (AOOs) shows that short, transient power excursions often demand only modest heat removal, and industry experience suggests that fuel can briefly enter dryout yet return to safe, stable operation. The lack of detailed understanding of the material response during such events motivates the present series of experiments. This study uses unique and innovative methods to investigate microstructural evolution in irradiated Zircaloy-2 exposed to high temperatures in inert environments. Differential Scanning Calorimetry (DSC) and FlashDSC are combined to build a comprehensive experimental framework capable of identifying the a–ß phase transformation in zirconium and examining defect annealing under steep thermal gradients. FlashDSC enables rapid heating and cooling of Focused Ion Beam (FIB)–prepared large-area lift-outs (LALOs) of irradiated Zircaloy-2 at rates of 1,000 K/s to peak temperatures of 600°C, 750°C, and 900°C. The goal is to determine whether these conditions produce measurable microstructural changes that could influence cladding performance in typical BWR environments. Microstructural characterization includes quantifying dislocation density and assessing secondary phase particle (SPP) size and distribution using Transmission Electron Microscopy (TEM). Ongoing analysis, such as diffraction pattern indexing and 4D STEM processing, will further refine these observations.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

Monitoring the long-term performance of organic redox flow battery by a distribution of relaxation time analysis

Organic redox flow batteries hold great promise as an energy storage technology, but their intricate chemistry makes them vulnerable to various degradation mechanisms. Monitoring this degradation is essential for identifying the limiting processes within the cells. Electrochemical impedance spectroscopy (EIS) offers a straightforward, in-situ method for measuring the total resistance of an operating cell. However, to pinpoint the limiting processes during long-term cycling, EIS data must be complemented by other techniques. Distribution of relaxation time (DRT) analysis is particularly effective for differentiating resistance components. Here, in this study, we perform a comprehensive analysis of resistance evolution and the separation of anode and cathode contributions during long-term cycling of a full cell employing 7,8-dihydroxyphenazine-2-sulfonic acid (DHPS) as the anolyte. Separate analyses of the DHPS anolyte and ferri-/ferrocyanide catholyte were conducted using a symmetric cell setup. The relaxation times derived from symmetric cells facilitate the identification of peaks in the DRT profiles from the full cell. Importantly, the DRT profiles indicate a correlation between the evolution of charge transfer resistance and the chemical degradation of DHPS. The methodologies and results outlined in this study offer significant insights for developing diagnostic tools applicable to other types of redox flow batteries.

Distribution of relaxation time↗
DOE OSTI2026

Recurrent convolutional neural networks for modeling nonadiabatic dynamics of quantum-classical systems

Recurrent neural networks (RNNs) have recently been extensively applied to model the time evolution in fluid dynamics, weather predictions, and even chaotic systems due to their ability to capture temporal dependencies and sequential patterns in data. Here we present an RNN model based on convolutional neural networks for modeling the nonlinear nonadiabatic dynamics of hybrid quantum-classical systems. The dynamical evolution of the hybrid systems is governed by equations of motion for classical degrees of freedom and von Neumann equation for electrons. The Physics-Aware Recurrent Convolution (PARC) neural network structure incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. Here, we apply our RNN approach to learn the space-time evolution of a one-dimensional semiclassical Holstein model after an interaction quench. For shallow quenches (small changes in electron-lattice coupling), the deterministic dynamics can be accurately captured using a single-CNN-based recurrent network. In contrast, deep quenches induce chaotic evolution, making long-term trajectory prediction significantly more challenging. Nonetheless, we demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.

Holstein model↗
DOE OSTI2025

An isotopic labeling investigation into the influence of the nitro group on LLM-105 thermal decomposition

Here, this work presents the first application of isotopically labeled LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) to investigate thermal decomposition pathways. Specially synthesized LLM-105 isotopologues were utilized to isolate the influence of labeled 15 NO 2 nitro groups on the formation of lightgas products. Simultaneous differential scanning calorimetry, thermo-gravimetric, and mass spectrometry measurements were employed to track the evolution of product gases, enabling the direct comparison of isotopically shifted species with unlabeled LLM-105. Key findings show that C 2 N 2 production is mainly dependent on nitrogen sources from either the amine groups or the pyrazine ring (i.e., not the nitro groups). The formation of NO, N 2 , and N 2 O all involves the nitro groups to some extent. NO (nitric oxide) was found to be the predominant gas species directly formed from the nitro group of LLM-105. In contrast, mixed nitrogen isotopologues of N 2 and N 2 O (i.e., 14 N 15 N and 15 NNO) formed more readily in comparison to their pure counterparts (i.e., 15 N 2 and 15 N 2 O). This indicates the amine and/or pyrazine groups of LLM-105, in addition to the nitro group, are involved in the decomposition pathways forming N 2 and N 2 O. In addition, our investigation led to the discovery of two previously unreported decomposition products (CHO and HNCO), which were confirmed through hydrogen labelling utilizing deuterium isotopes. These results provide detailed speciation trends of gaseous products during LLM-105 decomposition, offering new insights into reaction pathways. Experimental data reported here will support the development of a detailed chemical kinetics model for LLM-105, essential for the safe handling of high explosives.

Chemistry - Chemical explosives↗
DOE OSTI2026

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗
DOE OSTI2025

Understanding the Cathode Electrochemistry of Humidified Solid‐State Lithium‐Oxygen Batteries

Lithium-oxygen batteries (LOBs) possess a high theoretical energy density, making them potential candidates for next-generation energy storage. However, challenges such as reactive oxygen species-induced component degradation hinder their practical use. Inorganic solid-state electrolytes offer an alternative to degradation-prone aprotic electrolytes, while also protecting lithium anodes from potential atmospheric reactants. Here, this study explores the cathode electrochemistry of solid-state LOBs using humidified oxygen, which forms an aqueous catholyte during initial cycling, thereby improving cathode-electrolyte contact. To quantitatively analyze the cathode electrochemistry, a ‘Humidity-Incorporated’ Differential Electrochemical Gas Monitoring System (HiDEMS) is developed to control humidity and monitor gas consumption and evolution in real time. When studying a Li-O 2 cell that employs a NASICON-type Li 1.3 Al 0.3 Ti 1.7 (PO 4 ) 3 (LATP) solid electrolyte and a porous carbon cathode, a shift in discharge products from Li 2 O 2 to LiOH is observed over repeated cycles. While Li 2 O 2 evolves O 2 during charging, LiOH oxidation leads to minimal O 2 release and increased CO 2 production, originating from oxidation of carbon electrodes. Further, dissolution of Al and P from LATP is observed, likely driven by the formation of the alkaline catholyte. The findings highlight the need for carbon-free cathode materials and more stable solid-state conductors to minimize side reactions and improve rechargeability in humidified solid-state Li-O 2 batteries.

LATP degradation↗
DOE OSTI2025

Voltage Probability Density Function Shaping Control Strategy Considering Grid Operational Uncertainties

It is well-known that power systems operation always affected by various uncertainties which make the bus voltage a random process that can be characterized by its probability density function (PDF) at any time instant. In this context, this paper presents a novel PDF-based voltage control framework for power systems. By modeling voltage as a stochastic process, we formulate a stochastic differential equationthat captures grid uncertainties. The associated Fokker-Planck-Kolmogorov equation is derived to describe the evolution of the voltage PDF, which enables the formulation of a PDF-shaping control strategy. To simplify the PDF control formulation, a B-spline neural network is introduced for real-time estimation and regulation of the voltage distribution. The proposed PDF control law updates voltage references for energy storage systems and synchronous generators using real-time PDF measurements and feedback signals. The proposed method is validated on a modified Kundur’s two-area system. Simulation results demonstrate that the controller can significantly improve the voltage stability under stochastic conditions, highlighting its effectiveness in modern inverter-rich grids.

Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗
DOE OSTI2025

A small core in Vesta inferred from Dawn’s observations

Vesta’s large-scale interior structure had previously been constrained primarily using the gravity and shape data from the Dawn mission. However, these data alone still allow a wide range of possibilities for the differentiation state of the body. The moment of inertia is arguably the most diagnostic parameter related to the radial density distribution of a planetary body, making it crucial for assessing the body’s state of internal differentiation. Determining the moment of inertia requires additional measurements of the amplitudes of small rotational motions, such as precession and nutation. Here we report an updated estimate of the moment of inertia of Vesta inferred from Dawn’s Doppler tracking via the Deep Space Network and onboard imaging data. The recovered value for Vesta’s normalized polar moment of inertia is $\overline{C}$/MR 2 = 0.4208 ± 0.0047 (where M is the mass of Vesta and R is the reference radius), which is only 6.6% lower than the homogeneous value of 0.4505. This value, combined with the gravity field and global shape, suggests that Vesta’s interior has limited density stratification beneath its howardite–eucrite–diogenite-dominated crust. We propose two possible origin scenarios that are consistent with the observed constraints. In the first scenario, Vesta’s interior did not undergo full differentiation due to late accretion. In the second scenario, Vesta originated as an impact remnant of a larger differentiated body re-accreted with non-chondritic bulk composition produced from a catastrophic impact. Vesta did not experience complete differentiation in either scenario, suggesting that its current state reflects a complex interplay between its accretion timing, thermal evolution, redistribution of 26 Al bearing melt and/or impact processes.

CNEOS 2014-01-08 bolide↗
DOE OSTI2025

Nonintrusive projection-based reduced order modeling using stable learned differential operators

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where underlying governing equations are known but the access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a glass-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov–Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through four numerical experiments: 1-D scalar advection, 1-D Burgers, 2-D scalar advection and 1-D scalar advection–diffusion–reaction equations. In conclusion, the results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.

42 ENGINEERING↗