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This paper presents a mathematically rigorous, subspace projection-based reduced order modeling (ROM) methodology and an integrated framework to automatically generate reduced order models for spacecraft thermal analysis. Two key steps in the reduced order modeling procedure are described: (1) the acquisition of a full-scale spacecraft model in the ordinary differential equation (ODE) and differential algebraic equation (DAE) form to resolve its dynamic thermal behavior; and (2) the ROM to markedly reduce the dimension of the full-scale model. Specifically, proper orthogonal decomposition (POD) in conjunction with discrete empirical interpolation method (DEIM) and trajectory piece-wise linear (TPWL) methods are developed to address the strong nonlinear thermal effects due to coupled conductive and radiative heat transfer in the spacecraft environment. Case studies using NASA-relevant satellite models are undertaken to verify the capability and to assess the computational performance of the ROM technique in terms of speed-up and error relative to the full-scale model. ROM exhibits excellent agreement in spatiotemporal thermal profiles (<0.5% relative error in pertinent time scales) along with salient computational acceleration (up to two orders of magnitude speed-up) over the full-scale analysis. These findings establish the feasibility of ROM to perform rational and computationally affordable thermal analysis, develop reliable thermal control strategies for spacecraft, and greatly reduce the development cycle times and costs.
Bending tests provide a means to study plane strain fracture performance of 6000 series aluminum alloys. Metrics from bending tests have been correlated with self-pierce riveting (SPR) performance of a high strength AA6111 automotive aluminum alloy in previous works. Using the ORNL HPC resources, this project developed an innovative macro→micro←nano (MMN) multiscale microstructure-based finite element (FE) code to further understanding of the relationship between microstructure and fracture properties of high-strength 6000-series alloys. This work started with microstructural characterization in both mesoscale and nanoscale and bending performance characterization of AA6111 HS2-T6 alloy at Ford, the MMN framework was applied to this alloy to simulate 3-point VDA bending. From the results of the macro-modeling of 3-point VDA bending, the critical region of fracture was identified, and the region geometry was used to construct the micro-model. The fracture criterion of micron-scale precipitates and aluminum matrix which contains submicron and nano particles (AL-SMP-NP) in the micro-model was calibrated and validated by comparing simulated and measured bending results. With the AL-SMP-NP fracture strain obtained, the fracture strain of Al-matrix containing nano particles (ALNP) will similarly be determined by a submicron scale-model using an edge-constrained FE modeling approach developed by Hu et al. With the ALNP fracture strain obtained, the fracture strain of Al-matrix containing no particles will similarly be determined by a nano scale-model using an edge-constrained FE modeling approach. After the MMN framework is built and fracture criterion calibrated, nano-model FE simulations with virtual microstructures was performed to obtain a reduced order model (ROM) of the fracture criterion of the ALNP as a function of volume fraction, size, and distribution of the nanoparticle. This nano→submicron→micro modeling part allows exploration of the influence of different material nanostructures from different process conditions on the bending properties within the multiscale bending simulation framework and the ROM of material bendability as a function of nanoparticle size and shape was established. This obtained reduced order model (ROM) could help guide the design and selection of materials to improve existing SPR process models that could replace trial-and-error rivet/die selection and help to design new rivet/die combinations capable of robustly joining new higher strength 6000 5 series alloys in automotive body structures. This would enable lightweighting of Ford vehicles leading to greater fuel efficiency and reduce manufacturing time and energy.
Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.
The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).
Cooperative research and development activities at the NASA Langley Research Center (LaRC) involving reduced-order modeling (ROM) techniques are presented. Emphasis is given to reduced-order methods and analyses based on Volterra series representations, although some recent results using Proper Orthogonal Deco in position (POD) are discussed as well. Results are reported for a variety of computational and experimental nonlinear systems to provide clear examples of the use of reduced-order models, particularly within the field of computational aeroelasticity. The need for and the relative performance (speed, accuracy, and robustness) of reduced-order modeling strategies is documented. The development of unsteady aerodynamic state-space models directly from computational fluid dynamics analyses is presented in addition to analytical and experimental identifications of Volterra kernels. Finally, future directions for this research activity are summarized.
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.
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.
Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to provide numerical error bounds associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.
Thermal model correlation uses data from thermal balance tests to better estimate uncertain input parameter values. During the correlation process, input parameters are modified in an iterative manner which can become computationally expensive since this requires that the high-fidelity thermal model be run for each iteration. Depending on the number of thermal balance test points there can be many sets of correlation parameters that satisfy correlation criteria; and having enough data to ascertain the best set of correlation parameters to use, further increases the computational expense. Reduced-order models (ROMs) provide computationally efficient surrogates of high-fidelity models and are often built to reduce development cycle times and cost. By leveraging the speed of reduced-order models and the Correlation Analysis feature in the Veritrek software, the typical computational expense of a traditional thermal model correlation process can be significantly reduced and having access to hundreds of thousands of iteration results provides an advanced means of intelligently determining the best set of correlation parameters to use. The L’Ralph thermal team at NASA Goddard Space Flight Center explored the use of the Veritrek software for their thermal model correlation efforts. The ROM that was created allowed for the variation of 15 input parameters to match 70 temperature sensor readouts from 3 thermal balance plateus and required 125 runs of the high-fidelity Thermal Desktop® model to generate a ROM that could predict the detailed model’s results to within 0.2 K (RMS). The ROM was then used to find dozens of plausible correlation parameter values based on L’Ralph instrument test data within a few seconds. By providing several plausible correlation parameter combinations, Veritrek allowed the thermal team to explore different uncertain parameter value combinations and provided insight into how deterministic each input parameter was. This allowed for a more confident decision on the best set of correlation parameters to use, compared to traditional model correlation techniques. In this presentation, the L’Ralph thermal team will be presenting their experience with the Veritrek software and how the software was utilized to provide additional insights during the correlation process.
Thermal model correlation uses data from thermal balance tests to better estimate uncertain input parameter values. During the correlation process, input parameters are modified in an iterative manner which can become computationally expensive since this requires that the high-fidelity thermal model be run for each iteration. Depending on the number of thermal balance test points there can be many sets of correlation parameters that satisfy correlation criteria; and having enough data to ascertain the best set of correlation parameters to use, further increases the computational expense. Reduced-order models (ROMs) provide computationally efficient surrogates of high-fidelity models and are often built to reduce development cycle times and cost. By leveraging the speed of reduced-order models and the Correlation Analysis feature in the Veritrek software, the typical computational expense of a traditional thermal model correlation process can be significantly reduced and having access to hundreds of thousands of iteration results provides an advanced means of intelligently determining the best set of correlation parameters to use. The L’Ralph thermal team at NASA Goddard Space Flight Center explored the use of the Veritrek software for their thermal model correlation efforts. The ROM that was created allowed for the variation of 15 input parameters to match 70 temperature sensor readouts from 3 thermal balance plateus and required 125 runs of the high-fidelity Thermal Desktop® model to generate a ROM that could predict the detailed model’s results to within 0.2 K (RMS). The ROM was then used to find dozens of plausible correlation parameter values based on L’Ralph instrument test data within a few seconds. By providing several plausible correlation parameter combinations, Veritrek allowed the thermal team to explore different uncertain parameter value combinations and provided insight into how deterministic each input parameter was. This allowed for a more confident decision on the best set of correlation parameters to use, compared to traditional model correlation techniques. In this presentation, the L’Ralph thermal team will be presenting their experience with the Veritrek software and how the software was utilized to provide additional insights during the correlation process. "
Deterministic solutions to the Sn radiation transport equation can be computationally expensive to calculate. Reduced-order modeling enables efficient approximation of the full-order model (FOM) solution. We propose a novel method for constructing reduced-order models (ROMs) of the S n radiation transport equation, offline maximizing minimally invasive (OMMI) proper orthogonal decomposition (POD). POD uses the method of snapshots to create a reduced-order basis for constructing an ROM. Minimally invasive POD leverages the sweep infrastructure existing in deterministic transport codes to create a POD-based ROM, even when infeasible by traditional methods. Offline maximizing minimally invasive proper orthogonal decomposition (OMMI-POD) extends minimally invasive POD by performing sweeps offline, therefore maximizing the potential speedup. OMMI-POD does so by creating a library of reduced systems from a training set. This library of reduced systems is then interpolated to provide a rapid approximate solution of the S n radiation transport equation. The model is evaluated on a set of test problems, achieving a low error with a 466 times speedup over the FOM. Also presented is a study of the effect of sampling method on the performance of OMMI-POD, specifically comparing naive uniform sampling to the more accurate and computationally expensive greedy sampling.
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically accurate numerical simulations. The method can be applied to general nonlinear systems through the use of polynomial model form, while not requiring knowledge of the underlying physical model, governing equations, or numerical solvers. The process of learning ROMs is posed as a low-cost least-squares problem in a reduced-order subspace identified via Proper Orthogonal Decomposition (POD). Numerical experiments on classical pattern-forming systems–including the Schnakenberg and Mimura–Tsujikawa models–demonstrate that higher-order surrogate models significantly improve prediction accuracy while maintaining low computational cost. The proposed method provides a flexible, non-intrusive model reduction framework, well suited for the analysis of complex spatio-temporal pattern formation phenomena.
This study presents a reduced-order model (ROM) for computational fluid dynamics (CFD) simulations of cryogenic hydrogen isotope extrusions, focusing on protium (H₂) and deuterium (D₂) piston extruders. Using a 2D axisymmetric ROM in ANSYS-Polyflow, significant computational savings were achieved (runtime reduced from 9∼24 h to 3∼5 min), with extrusion force discrepancies between the 2D ROM and 3D models being on the order of 1%. Parametric studies identified optimal cutoff shear rates in the viscosity model (0.01/s for H₂ and 0.001/s for D₂), providing recommendations for future simulations. Finally, a comprehensive comparison of ROM results with experimental data was performed across varying geometries, cryogenic materials, temperatures, extrusion lengths, and piston velocities. Predictions at low extrusion temperatures met the objective of providing quick and efficient solutions with an acceptable extrusion force error of approximately 10% or less, validating the effectiveness of the 2D ROM approach. However, at high temperatures closer to the triple point, extrusion force error grows, which necessitates developing an improved model that accounts for temperature effects, e.g. melting. Nevertheless, the findings still represent a significant improvement in efficiency of CFD modeling of cryogenic hydrogenic extrusion. The ROM framework can also be extended to tritium (T2) and screw extruders, which will ultimately provide a fast and effective tool for optimizing pellet injector design for ITER and future reactor systems.
Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.
Fluid reduced-order models (ROMs) which capture the flow physics within the problem's physical domain are usually constrained in accuracy to only the parameter points, e.g. Reynolds and Mach numbers, at which reference data was provided. Interpolation-focused quantity-of-interest ROMs are often structured differently and fail to provide flow volume data with the same quality - if at all. In this paper, techniques which reside at the intersection of these two ROM schools - flow physics ROMs which can be interpolated within a parameter space of interest - are explored. Using a combination of existing and novel techniques, emergent physics are identified using a fluid ROM at parameter points which are not provided in the ROM's training data.
Fluid reduced-order models (ROMs) which capture the flow physics within the problem's physical domain are usually constrained in accuracy to only the parameter points, e.g. Reynolds and Mach numbers, at which reference data was provided. Interpolation-focused quantity-of-interest ROMs are often structured differently and fail to provide flow volume data with the same quality - if at all. In this paper, techniques which reside at the intersection of these two ROM schools - flow physics ROMs which can be interpolated within a parameter space of interest - are explored. Using a combination of existing and novel techniques, emergent physics are identified using a fluid ROM at parameter points which are not provided in the ROM's training data.
Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROMs). To demonstrate the potential of this combination, in this paper, we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the “optimize-then-reduce” path toward solving the minimization problem at each time step and solve reduced space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for an efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. In conclusion, we present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.