Reduced-order Model Research Articles (Page 1)

Abstract In this paper we investigate large-scale linear systems driven by a fractional Brownian motion (fBm) with Hurst parameter $H\in [1/2, 1)$ . We interpret these equations either in the sense of Young ( $H>1/2$ ) or Stratonovich ( $H=1/2$ ). In particular, fractional Young differential equations are well suited to modeling real-world phenomena as they capture memory effects, unlike other frameworks. Although it is very complex to solve them in high dimensions, model reduction schemes for Young or Stratonovich settings have not yet been much studied. To address this gap, we analyze important features of fundamental solutions associated with the underlying systems. We prove a weak type of semigroup property which is the foundation of studying system Gramians. From the Gramians introduced, a dominant subspace can be identified, which is shown in this paper as well. The difficulty for fractional drivers with $H>1/2$ is that there is no link between the corresponding Gramians and algebraic equations, making the computation very difficult. Therefore we further propose empirical Gramians that can be learned from simulation data. Subsequently, we introduce projection-based reduced-order models using the dominant subspace information. We point out that such projections are not always optimal for Stratonovich equations, as stability might not be preserved and since the error might be larger than expected. Therefore an improved reduced-order model is proposed for $H=1/2$ . We validate our techniques conducting numerical experiments on some large-scale stochastic differential equations driven by fBm resulting from spatial discretizations of fractional stochastic PDEs. Overall, our study provides useful insights into the applicability and effectiveness of reduced-order methods for stochastic systems with fractional noise, which can potentially aid in the development of more efficient computational strategies for practical applications.

Inverse Scattering for Schrödinger Equation in the Frequency Domain via Data-Driven Reduced Order Modeling

Purpose This study aims to improve simulation efficiency for status and fault monitoring in gas seal systems. Design/methodology/approach A rapid calculation method for seal flow fields based on non-invasive model order-reduction is proposed. First, training data were obtained by calculating sample working conditions in the full-order model (FOM) with a typical spiral groove gas seal as the research object. Then, singular value decomposition and genetic aggregation algorithms were used to perform dimensionality reduction and interpolation fitting on the training data. Finally, select an appropriate sample size and the number of modes for constructing a reduced-order model (ROM) based on error prediction. A flow field ROM consisting of working condition-modal coefficients and modal bases is established. Findings The simulation performance of the ROM is evaluated by the error of results between the FOMs and ROMs. The results of this study indicate that the absolute error of the seal face pressure prediction does not exceed 0.01 MPa, with a maximum relative error below 0.3%. The maximum pressure in the slot area increased by 59.57% compared to the inlet pressure. In addition, the calculation time for the ROM has been reduced to less than 1 s. Originality/value The data-driven flow field ROM described in this paper provides method support for model simplification and the construction of gas seal digital twins, effectively solving the problem of real-time monitoring and fault detection in gas seal systems. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2025-0288/

This paper presents a comprehensive study of multi-degree-of-freedom (MDOF) structural vibration and projectiletarget penetration dynamics using analytical, numerical, and simulation-based approaches. For the undamped three-degree-of-freedom massspring system, equations of motion were derived and expressed in matrix form, enabling the determination of natural frequencies, mode shapes, and unknown mass parameters. This analysis verified the models validity and demonstrated the fundamental characteristics of MDOF vibration systems. In parallel, a reduced-order projectiletarget model was developed, coupling rigid-body motion with axial vibration through equivalent stiffness and damping. Analytical derivations, MATLAB simulations, and Python-based nonlinear modeling highlighted the roles of damping, elastic compression, and resistance forces in penetration dynamics. To validate these findings, finite element simulations using ANSYS/Autodyn were performed, capturing projectile deformation, energy dissipation, and penetration depth. The results collectively confirm that simplified models, when cross-validated with high-fidelity simulations, can effectively capture the essential physics of vibration and impact, offering practical insights for engineering design, vibration control, and protective structure development.

Grid-scale lithium-ion storage must deliver fast, reliable thermal control during dynamic grid services, yet high-fidelity thermal models are too slow for real-time use and inefficient cooling inflates energy and safety costs. This study develops and validates a reduced-order thermal modeling framework for grid-scale lithium-ion battery energy storage, targeting real-time thermal management. The framework uses proper orthogonal decomposition to capture dominant thermal dynamics across frequency regulation, peak shaving, and fast charging. Across scenarios, it delivers 15.2–22.3× computational speedups versus a detailed model while maintaining RMS temperature errors of 7.8 °C (frequency regulation), 34.4 °C (peak shaving), and 23.3 °C (fast charging). Spatial analysis identifies inter-zone temperature gradients up to 1.0 °C under severe loading, motivating targeted cooling strategies. Cooling energy scales nonlinearly with load intensity, from 5.44 kWh in frequency regulation to over 300 kWh in peak shaving, with cooling efficiencies spanning 17.27% to 8.94%. The reduced-order model achieves sub-0.1 s computational solve time per control cycle, suggesting feasibility for real-time integration into industrial battery-management systems under the tested simulation settings. Collectively, the results show that reduced-order thermal models can balance accuracy and computational efficiency for several grid services in the simulated scenarios, while high-power operation benefits from scenario-specific calibration and controller tuning. Practically, the benchmarks and workflow support decisions on predictive cooling schedules, temperature limits, and service prioritization to minimize parasitic energy.

Abstract Large eddy simulation reduced order models (LES-ROMs) are ROMs that leverage LES ideas (e.g., filtering and closure modeling) to construct accurate and efficient ROMs for convection-dominated (e.g., turbulent) flows. Eddy viscosity (EV) ROMs (e.g., Smagorinsky ROM (S-ROM)) are LES-ROMs whose closure model consists of a diffusion-like operator in which the viscosity depends on the ROM velocity. We propose the Ladyzhenskaya ROM (L-ROM), which is a generalization of the S-ROM. Furthermore, we prove two fundamental numerical analysis results for the new L-ROM and the classical S-ROM: (i) We prove the verifiability of the L-ROM and S-ROM, i.e., that the ROM error is bounded (up to a constant) by the ROM closure error. (ii) We introduce the concept of ROM limit consistency (in a discrete sense), and prove that the L-ROM and S-ROM are limit consistent, i.e., that as the ROM dimension approaches the rank of the snapshot matrix, d , and the ROM lengthscale goes to zero, the ROM solution converges to the “true solution" , i.e., the solution of the d -dimensional ROM. Finally, we illustrate numerically the verifiability and limit consistency of the new L-ROM and S-ROM in two under-resolved convection-dominated problems that display sharp gradients: the 1D Burgers equation with a small diffusion coefficient; and the 2D lid-driven cavity flow at Reynolds number $$\textrm{Re}=15,000$$ Re = 15 , 000 .

Transonic buffet is a complex and strongly nonlinear unstable flow sensitive to variations in the incoming flow state. This poses great challenges for establishing accurate-enough reduced-order models, limiting the application of model-based control strategies in transonic buffet control problems. To address these challenges, this paper presents a time-variant modelling approach that incorporates rolling sampling, recursive parameter updating and inner iteration strategies under dynamic incoming flow conditions. The results demonstrate that this method successfully overcomes the difficulty in designing appropriate training signals and obtaining unstable steady base flow. Additionally, it improves the global predictive capability and identification efficiency of linear models for nonlinear flow-system responses by more than one order of magnitude. Furthermore, two adaptive control strategies – minimum variance control and generalised predictive control – are validated as effective based on the time-variant reduced-order model through numerical simulations of the transonic buffet flow over the NACA 0012 aerofoil. The adaptive controllers effectively regulate the unstable eigenvalues of the flow system, achieving the desired control outcomes. They ensure that the shock wave buffet phenomenon does not recur after control is applied, and that the actuator deflection, specifically the trailing-edge flap, returns to zero. Moreover, the control results further confirm the global instability essence of transonic buffet flow from a control perspective, thereby deepening the cognition of this nonlinear unstable flow.

Developing a reduced order model for pulsatile blood flow simulations using minimal three-dimensional simulation data.

Cochlear implants successfully treat severe to profound hearing loss patients. Patient-specific numerical simulations can yield important insights that could guide surgical planning and the interpretation of post-operative measurements. However, these simulations have a high computational effort. A non-intrusive reduced-order model has been used to replace the patient-specific model generation and simulation of different electrical stimulation sources, reducing the computational time and enabling fast response simulations. The reduced-order model combines proper orthogonal decomposition with radial basis function interpolation. The dataset used to build the reduced order model consists of 528 different solutions, also referred to as snapshots, from 24 cochlear models, with each cochlea subjected to 22 simulations with varying electrical stimuli. Each simulation is characterized by five parameters, three specifying the cochlea geometry and two specifying the electrode array position and the active electrode. A leave-one-out strategy was used to verify the accuracy of the reduced-order model. The presented approach reduces the time for the patient-specific model generation and simulation from nearly 1.5 hours to less than a second while providing a high accuracy of the solutions with a relative error of 2.5% compared to the finite element solution. The presented non-intrusive reduced order model can predict the 3D intracochlear voltage distribution for new patients and implant positions. This work demonstrates the feasibility of fast patient-specific simulations. These numerical investigations could support the fitting of cochlear implants, the design of individualized sound coding strategies and surgery-dependent decision-making.

Buzz is a critical concern in aeroelasticity in modern aircraft design. It stems from the coupling of flow and structural modes, causing structural instability. As wings grow larger, aeroelastic effects gain more significance, especially the influence of the structural mode of the main wing with higher flexibility on the buzz characteristics. Based on two-dimensional three-degree-of-freedom airfoils, this paper delves into how the plunge and pitch modes affect flap buzz in buffeting flows. Using an aeroelastic model based on a reduced-order model (ROM) and CFD/CSD time-domain simulations, the study shows that airfoil structural modes notably impact flap buzz. The plunge-flap deflection coupling is weak, yet the plunge mode enlarges the instability range of the flap deflection mode. Conversely, the pitch-flap deflection coupling is strong, and the pitch mode shrinks the instability range of the flap deflection mode. Notably, the ratio of flap deflection frequency to plunge frequency has negligible effects on the instability of the flap deflection mode, while the ratio of flap deflection frequency to pitch frequency has significant impacts on it. Adjusting the ratio between the structural frequency and the flap deflection frequency can be an effective strategy for avoiding buzz.

Reduced-order modeling and optimization of sandwich pipe beams with graded corrugated cores based on the mechanics of structure genome

Abstract Subsurface geometries, such as faults and subducting slab interfaces, are often poorly constrained, yet they exert first‐order control on key geophysical processes, including subduction zone thermal structure and earthquake rupture dynamics. Quantifying model sensitivity to geometric variability remains challenging for high‐fidelity simulations that require generated meshes, due to the manual effort of mesh generation and the computational cost of exploring high‐dimensional parameter spaces. We present a mesh morphing approach that deforms a reference mesh into geometrically varying configurations while preserving mesh connectivity. This enables the automated generation of large ensembles of geometrically variable meshes with minimal user input. Importantly, the preserved connectivity allows for the application of data‐driven, non‐intrusive reduced‐order models (ROMs) to perform robust sensitivity analysis and uncertainty quantification. We demonstrate mesh morphing in two geophysical applications: (a) 3D dynamic rupture simulations with fault dip angles varying across a 40° range, and (b) 2D thermal models of subduction zones incorporating realistic slab interface curvature and depth uncertainties. The morphed meshes retain high quality and lead to accurate simulation results that closely match those obtained using generated meshes. For the dynamic rupture case, we construct ROMs that efficiently predict surface displacement and velocity time series as functions of fault geometry, achieving speedups of up to times relative to full simulations. Our results show that mesh morphing can be a powerful and generalizable tool for incorporating geometric uncertainty into physics‐based modeling. The method supports efficient ensemble modeling for rigorous sensitivity studies applicable across a range of problems in computational geophysics.

Consistent reduced order modeling for wind turbine wakes using variational multiscale method and actuator line model

Simple-Multi-Attribute-Rating-Technique Assisted Reduced Order Modeling of Fuel Cell Integrated Autonomous Microgrid Ensuring Stability and Zero Steady State Error

Research on digital twin of three-dimensional reduced order model of marine composite propeller blades based on multisensory fusion

A novel reduced order model of circulating fluidized beds coupled with enhanced compressed sensing and temporal convolutional neural networks

Symbolic regression of data-driven reduced order model closures for under-resolved, convection-dominated flows

A universal parametric nonlinear model order reduction method for complex shell structures

A hybrid reduced-order model for dynamic analysis of self-deployable shell-membrane structures

Structural Reduced-Order Model including Geometrical Nonlinearities and Application to Aeroelastic Behavior Analysis