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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Leveraging Optimal Sparse Sensor Placement to Aggregate a Network of Digital Twins for Nuclear Subsystems

Nuclear power plants (NPPs) require continuous monitoring of various systems, structures, and components to ensure safe and efficient operations. The critical safety testing of new fuel compositions and the analysis of the effects of power transients on core temperatures can be achieved through modeling and simulations. They capture the dynamics of the physical phenomenon associated with failure modes and facilitate the creation of digital twins (DTs). Accurate reconstruction of fields of interest (e.g., temperature, pressure, velocity) from sensor measurements is crucial to establish a two-way communication between physical experiments and models. Sensor placement is highly constrained in most nuclear subsystems due to challenging operating conditions and inherent spatial limitations. This study develops optimized data-driven sensor placements for full-field reconstruction within reactor and steam generator subsystems of NPPs. Optimized constrained sensors reconstruct field of interest within a tri-structural isotropic (TRISO) fuel irradiation experiment, a lumped parameter model of a nuclear fuel test rod and a steam generator. The optimization procedure leverages reduced-order models of flow physics to provide a highly accurate full-field reconstruction of responses of interest, noise-induced uncertainty quantification and physically feasible sensor locations. Accurate sensor-based reconstructions establish a foundation for the digital twinning of subsystems, culminating in a comprehensive DT aggregate of an NPP.

42 ENGINEERING↗
DOE OSTI2024

Lower length scale model for palladium attack of silicon carbide in TRISO fuel

TRistructural ISOtropic (TRISO) particle fuels rely on silicon carbide (SiC) as the primary barrier for metallic fission product (FP) release. Palladium (Pd) generated by fission degrades the SiC layer, resulting in the formation of lamellar layers of palladium silicides (PdxSi) and carbon (C) perpendicular to the direction of attack. The Pd attack has been hypothesized to be responsible for failure of the SiC layer and enhance FP release. To better understand and quantify Pd attack of SiC in TRISO particles, a multiscale, mechanistic model of Pd transport is being developed by the NEAMS program. Previous work provided an initial hypothesis for modeling lamellar microstructure formation in SiC due to Pd attack using a phase-field model. The work described in this report builds on the previous model by using molecular dynamics (MD) simulations to parameterize the phase-field model kinetics, and build a reduced order model in BISON using the improved mesoscale Pd penetration model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Development of a Techno-Economic Analysis Framework for a Solar Thermochemical Fuel Production Process

Synthetic liquid fuels can provide a drop-in substitute for fossil-based fuels in sectors such as aviation and maritime, where electrification is not a viable option due to the need for high specific energy density. However, for these alternative fuels to be adopted at a commercial scale, their price must be competitive compared to their fossil-based counterparts. The reverse water-gas shift (RWGS) reaction offers a promising pathway, using hydrogen (sourced from electrolysis) and carbon dioxide as the feed and reacting to produce syngas - a mixture of H2 and CO at a specific ratio. Syngas is a useful precursor that can be converted into fuels and chemicals via known downstream processes, such as liquid transportation fuels via Fischer-Tropsch (FT) synthesis. The RWGS reaction is currently not applied in commercial scale, unlike the rest of the components in the process chain (electrolyzers and syngas-to-fuel synthesis units). The RWGS reaction poses several challenges due to its restrictive thermodynamics. Being an equimolar reaction, high temperatures and a large excess of H2 are needed to achieve reasonable CO2 conversion at equilibrium. This has detrimental effects on practical process implementation and the quality of syngas that can be produced, with direct effect on the energy and capital requirements, as well as the need for expensive downstream separation. In this work, we are proposing to develop a new concentrating solar thermal (CST) compatible RWGS reactor, performing the reaction in a 2-step chemical looping process using metal oxide at a temperature range of 600-800 degrees Celsius. By decoupling the reactor from the solar receiver, the Generation 3 (Gen3) CST technology could be utilized, together with its proposed thermal energy storage (TES) technology, benefitting from a good match to the required temperatures. CST technology is a viable option for supplying the heat that could be rapidly deployed in scale, thus being a good match to the gas-to-liquid (GTL) process which requires a large minimal scale to be commercially viable. The integration of TES with CST also allows operating the plant at large annual capacity factors and avoids multiple shutdown/startup cycles, thus fitting into the steady-state operation mode that most GTL processes require. The main innovation in the proposed design hinges on a countercurrent reaction design using a packed bed reactor. In 2019 Metcalfe et al. showed the benefits of countercurrent species exchange could be realized in a redox chemical-looping processes, by storing the favorable countercurrent chemical potential profiles in a packed bed of non-stoichiometric oxide. Metcalfe et al. applied this breakthrough concept to the WGS reaction, which is conventionally a co-feed catalytic process, showing a dramatic improvement. Bulfin et al. (2023) performed a similar proof-of-concept demonstration for the RWGS reaction using CeO2, achieving cumulative and peak CO2 conversions of 88% and 95%, respectively, compared to a thermodynamic limit of 58% for the co-feed catalytic process at the same conditions. In our new REGENLOOP project, we are developing a reactor prototype from the heat-exchange packed bed reactor-type, a commonly used reactor in the chemical industry. The endothermic heat of reduction will be supplied to the reactor using CST, while the same heat transfer fluid (HTF) mechanism will be used to extract the exothermic heat of oxidation. An array of multiple reactors is used to supply constant high-purity CO stream, that is then mixed with H2 from electrolysis to produce a high-purity syngas at the required composition. By removing the CO-CO2 separation after the RWGS process, significant energy and cost reduction can be achieved. A physics-based TEA framework is currently being developed, covering all the major plant processes, from the solar collection through storage, chemical looping RWGS, GTL, and auxiliary unit operations, up to the liquid hydrocarbon product. This modeling framework will utilize reduced-order models for the chemical looping RWGS and TES, CST modeling using SolarPILOT, and Aspen Plus for the GTL. By using this combined physics-based approach, the effects of design/operating parameters on the performance and cost can be elucidated. In our presentation, the modeling framework will be presented in detail, including preliminary cost predictions of using this plant configuration under a few selected relevant case studies. This study will be used to identify the major cost drivers, informing further system design and optimization needed to chart the way for a commercially viable pathway.

14 SOLAR ENERGY↗
DOE OSTI2025

Genetic programming for the nuclear many-body problem: a guide

Genetic Programming (GP) is an evolutionary algorithm that generates computer programs, or mathematical expressions, to solve complex problems. In this Guide, we demonstrate how to use GP to develop surrogate models to mitigate the computational costs of modeling atomic nuclei with ever increasing complexity. The computational burden escalates when uncertainty quantification is pursued, or when observables must be globally computed for thousands of nuclei. By studying three models in which the mean field depends on the total particle density self-consistently, we show that by constructing reduced order models supported by GP one can speed up many-body computations by several orders of magnitude with a negligible loss in accuracy.

dimensionality reduction↗
DOE OSTI2024

Data-scarce surrogate modeling of shock-induced pore collapse process

Understanding the mechanisms of shock-induced pore collapse is of great interest in various disciplines in sciences and engineering, including materials science, biological sciences, and geophysics. However, numerical modeling of the complex pore collapse processes can be costly. To this end, a strong need exists to develop surrogate models for generating economic predictions of pore collapse processes. Here, in this work, we study the use of a data-driven reduced-order model, namely dynamic mode decomposition, and a deep generative model, namely conditional generative adversarial networks, to resemble the numerical simulations of the pore collapse process at representative training shock pressures. Since the simulations are expensive, the training data are scarce, which makes training an accurate surrogate model challenging. To overcome the difficulties posed by the complex physics phenomena, we make several crucial treatments to the plain original form of the methods to increase the capability of approximating and predicting the dynamics. In particular, physics information is used as indicators or conditional inputs to guide the prediction. In realizing these methods, the training of each dynamic mode composition model takes only around 30 s on CPU. In contrast, training a generative adversarial network model takes 8 h on GPU. Moreover, using dynamic mode decomposition, the final-time relative error is around 0.3% in the reproductive cases. We also demonstrate the predictive power of the methods at unseen testing shock pressures, where the error ranges from 1.3 to 5% in the interpolatory cases and 8 to 9% in extrapolatory cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Physics-Reinforced Machine Learning Algorithms for Multiscale Closure Model Discovery

The central objective of this project was to address the challenge of modeling and simulating complex multiscale turbulence phenomena by leveraging physics-guided machine learning (PGML) and hybrid modeling approaches. By integrating physics-based methods with data-driven models, the research focused on achieving robust and scalable solutions for geophysical turbulence, enhancing numerical weather prediction and climate research tools. The project resulted in significant advancements in computational modeling paradigms, predictive tools for reduced-order modeling, and innovative algorithms for fluid dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Conjugate Heat Transfer Modeling of Salt-Filled Fuel Pins for Stable Salt Reactor Safety Analysis

The Stable Salt Reactor (SSR) combines the proven structural design of light water reactor fuel assemblies with the inherent safety and fuel-cycle advantages of molten salt technology. In its fast reactor configuration, the SSR utilizes recycled nuclear waste as fuel, sealed within narrow salt-filled fuel pins and cooled by a surrounding liquid salt coolant. Reliable transfer of heat from the molten fuel salt through the cladding to the external coolant is essential for both reactor safety and performance. This work investigates conjugate heat transfer (CHT) in the SSR’s salt-filled fuel pins using NekRS, a high-fidelity spectral element computational fluid dynamics (CFD) solver. The analyses capture internal natural convection within the molten fuel salt and external forced convection in the coolant, under steady-state and transient operating conditions. Parametric studies evaluate how variations in reactor power and coolant flow rate influence heat transfer distributions and system response. The high-fidelity CFD results are time-averaged and post-processed for direct comparison with moderate-fidelity Reynolds-averaged Navier–Stokes (RANS) models, and for the development of reduced-order models within the SAM system code. These validated models support fast-running safety analyses of normal and off-normal transients, improving predictive capability for key safety margins. By integrating advanced CFD with system-level safety tools, this study strengthens the modeling framework for SSR design, reduces uncertainty in molten salt CHT simulations, and accelerates the engineering and licensing of next-generation nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Deep learning model for fast, science-based forecasting of fluid migration along faults in geologic carbon storage scenarios

Effective long-term geologic storage depends on robust site selection and credible, science-based forecasting of subsurface behavior to ensure storage integrity. For this work, we develop a deep learning–based reduced-order model (ROM) to quantify potential carbon dioxide (CO₂) and brine migration through geological faults. The ROM combines a Transformer model for binary classification and a Stacked Ensemble for regression, trained on a comprehensive dataset generated from 1400 physics-based reservoir simulations. Key geologic and operational parameters—including fault geometry, reservoir structure, and injection conditions—were systematically varied to capture a wide range of fluid migration scenarios. The ROM accurately predicts the onset of migration, cumulative migration volumes of both CO₂ and brine, and associated migration rates, as compared to an independent set of validation simulations, while significantly reducing computational cost compared to traditional simulation methods. Model performance was evaluated across diverse fault configurations, revealing that shallow reservoir geometry and fault angle are among the most influential factors governing migration behavior. Sensitivity analysis using SHapley Additive exPlanations (SHAP) provided interpretability, revealing distinct patterns in how geological and operational features drive transient versus cumulative migration outcomes. The ROM’s ability to rapidly simulate fault migration scenarios enables efficient sensitivity analyses, scenario evaluations, and decision support for site selection and monitoring design. This approach enhances the safety, scalability, and long-term operational performance of geologic carbon storage (GCS) systems by providing a robust, interpretable tool for predicting subsurface fluid migration and assessing fault-related migration potential.

42 ENGINEERING↗
DOE OSTI2025

A predictive analytical model of electrical transport in multi-principal-element alloys

A predictive analytical model is presented for the electrical conductivity of multi-principal-element alloys (MPEAs), including those containing aluminum, transition metals, and refractory metals. Given that the lattice parameter of the Wigner-Seitz cell of an MPEA is similarly variable to a bulk metallic glass, it is postulated that electron scattering can be approximated by a series of two-level systems. Here, the resulting reduced-order model enabled an accurate determination of electrical resistivity and electron thermal conductivity based on the scattering of electrons in a two-level system across a Bloch-potential-based virtual crystal approximation. Model results are compared to experimental four-point probe electrical resistivity measurements between 300 K and 700 K for Al 0.3 CoCrCuFeNi, CoCrFeMnNi, (CoCrFeMnNi) 0.98 W 0.02 , (CoCrFeMnNi) 0.95 W 0.05 , and Nb 4 Ta 4 V 3 Ti, for model validation.

Analytical model↗
DOE OSTI2024

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Ensemble Kalman filter for data assimilation coupled with low-resolution computations techniques applied in fluid dynamics

This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.

Data Assimilation↗
DOE OSTI2026

Hydrodynamic Analysis and Optimization of Aquantis Marine Turbine: Cooperative Research and Development (Final Report)

The primary aim of this proposal is to improve the accurate prediction of hydrodynamic performance and dynamic load responses of the AQ10 floating axial-flow tidal turbine with a tri-cat mooring configuration. The validation of reduced-order modeling approaches with high-fidelity model will be implemented. Additionally, the frequency response domain, Response Amplitude Floating Wind (RAFT) toolbox plus an optimizer expanded for marine hydrokinetic turbines under the Submarine Hydrokinetic And Riverine Kilo-megawatt. Systems (SHARKS) program will be used for designing and exploring different key design parameters (platform dimension, mooring layout and its parameters) of next marine hydrokinetic (MHK) turbine generation.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Data-Driven Analysis of Multipactor Dynamics via Dynamic Mode Decomposition

Multipactor effect is a performance-limiting kinetic plasma effect that can occur in high-power microwave and radio frequency (RF) devices. Multipactor effect is of special concern in vacuum or near-vacuum conditions such as those in particle accelerators and spaceborne devices. In this work, we present a data-driven reduced-order model (ROM) based on dynamic mode decomposition (DMD) for modeling of multipactor effects. We study multipactor effects and the resulting nonlinear harmonic generation by processing high-fidelity data generated from electromagnetic particle-in-cell (EMPIC) simulations using the DMD algorithm. We also investigate time-delay embedding extensions of DMD with improved generalizability and accuracy for modeling the electron plasma current density behavior. Here, the results show that DMD provides valuable insights into multipactor phenomena by extracting relevant modal spatiotemporal patterns and frequencies. In addition, DMD offers the potential to time extrapolate EMPIC simulations at a minimal cost, thereby reducing overall simulation time.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Latent space dynamics identification for interface tracking with application to shock-induced pore collapse

Capturing sharp, evolving interfaces remains a central challenge in reduced-order modeling, especially when data is limited and the system exhibits localized nonlinearities or discontinuities. Here, we propose LaSDI-IT (Latent Space Dynamics Identification for Interface Tracking), a data-driven framework that combines low-dimensional latent dynamics learning with explicit interface-aware encoding to enable accurate and efficient modeling of physical systems involving moving material boundaries. At the core of LaSDI-IT is a revised autoencoder architecture that jointly reconstructs the physical field and an indicator function representing material regions or phases, allowing the model to track complex interface evolution without requiring detailed physical models or mesh adaptation. The latent dynamics are learned through linear regression in the encoded space and generalized across parameter regimes using Gaussian process interpolation with greedy sampling. We demonstrate LaSDI-IT on the problem of shock-induced pore collapse in high explosives, a process characterized by sharp temperature gradients and dynamically deforming pore geometries. The method achieves relative prediction errors below 9% across the parameter space, accurately recovers key quantities of interest such as pore area and hot spot formation, and matches the performance of dense training with only half the data. This latent dynamics prediction was 10 6 times faster than the conventional high-fidelity simulation, proving its utility for multi-query applications. These results highlight LaSDI-IT as a general, data-efficient framework for modeling discontinuity-rich systems in computational physics, with potential applications in multiphase flows, fracture mechanics, and phase change problems.

Gaussian process↗
DOE OSTI2025

Risk assessment of wellbore leakage during underground hydrogen storage

The expansion of renewable energy sources would require large-scale energy storage options to overcome the intermittent nature of these sources. Underground hydrogen storage (UHS) in depleted hydrocarbon reservoirs offers a scalable and practical energy storage solution. These reservoirs are chosen for their availability and large capacity, but the unique properties of hydrogen raise concerns about potential leakage pathways, particularly through wellbores. In this study, we develop and apply, for the first time, reduced-order models (ROMs) specifically designed for efficient leakage risk prediction in UHS systems operating in depleted hydrocarbon reservoirs. Using 3,000 high-fidelity simulation scenarios, we examine the influence of 11 key parameters, including reservoir and aquifer depths, wellbore permeability and porosity, initial saturations of water, oil and gas fractions (hydrogen, light, intermediate, and heavy hydrocarbons), reservoir pressure multiplier, and the aquifer-to-reservoir volume ratio, to simulate leakage behavior over a 1,000-year timescale. We train ROMs using a two-step classification-regression approach, achieving R 2 values exceeding 99 % across all targets. These ROMs effectively capture the leakage evolution and identify critical controls of leakage, guiding the design of mitigation strategies. Results indicate that gas leakage occurs in about 27 % of scenarios as early as five years post-operation, reaching volumes of up to 106 ft3. Oil leakage is less frequent (~17 %) and typically begins decades later. Our findings also show that hydrogen often migrates first, owing to its smaller molecular size and higher buoyancy, followed by heavier hydrocarbons. Over time, these heavier components contribute significantly to the total leaked volume, reinforcing the need for targeted monitoring and remediation strategies. Our analysis highlights that deeper storage reservoirs, shallower aquifers, and low-permeability wellbores significantly reduce leakage risks. In conclusion, this work offers a robust framework for risk-informed UHS deployment, supporting energy security through reliable large-scale hydrogen storage while safeguarding environmental integrity.

08 HYDROGEN↗
DOE OSTI2026

Statistical Correlation of Heliostat Pointing Deviation With Wind

This work was carried out as part of the Heliostat Consortium (HelioCon) Field Deployment subtask with the aim to develop a reduced order model framework for correlating wind speed and pointing deviation of a heliostat facet. There are only sparse field measurements of heliostat pointing deviations and accompanying wind conditions published in the literature. Heliostat test standards, such as IEC 62862-4-3, propose a suite of tests including laser pointing repeatability at wind speeds below 4 m/s, and provide technical requirements for heliostat slope and tracking deviations in coarse average wind speed bins of 4 m/s, 6 m/s, and 8 m/s. In addressing the gap of the variation of heliostat pointing deviation with wind speed, field measurements of laser pointing on a grid target and wind conditions were analyzed in this study at the Third-Party Metrology Platform at the National Laboratory of the Rockies (NLR) Flatirons Campus. Horizontal pointing deviations were found to follow a logarithmic relationship with peak wind speed, whereas vertical pointing deviations follow an exponential relationship with peak wind speed. Both horizontal and vertical pointing deviations also follow a second order polynomial relationship, as expected from the proportionality of elastic loads and deformations with the square of wind speed. The results indicate that heliostat facet pointing deviations in the vertical direction increase at a faster rate than in the horizontal direction with increasing wind speed over the tested range, however these are dependent on the heliostat structural design. Next steps are recommended for additional field measurements to confirm a linear relationship of pointing deviation with applied moment on a heliostat facet, and to distinguish between gravity-induced and wind-induced pointing deviations at different elevation angles. The derived correlations in the preliminary analysis in this report serve as a case study for heliostat developers and plant operators to estimate the wind-induced pointing deviations and their variation with peak gust wind speed. Next steps in future work would recommend higher resolution and longer duration datasets for different elevation angles and wind directions to reduce uncertainties and variance of collected laser beam spot data and their correlations with bin-averaged wind speed.

17 WIND ENERGY↗
DOE OSTI2025

mphys-surrogate-model

This repository contains python scripts for building and studying reduced-order-modeling representations of droplet coalescence for eventual use in atmospheric models. The included data are generated from high-fidelity superdroplet methods and are utilized by machine learning pipelines to build data-driven models of droplet size distributions that evolve under coalescence. This repository further includes scripts to determine prediction (uncertainty) intervals on the data-driven model products based on conformal prediction.

Katona, JonasE [Lawrence Livermore National Labora↗
DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗