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1. A non-intrusive reduced order model using deep learning for realistic wind data generation for small unmanned aerial systems in urban spaces

   https://doi.org/10.1063/5.0098835  

   Vuppala, Rohit_K_S_S; Kara, Kursat (August 2022, AIP Advances)

   Realistic wind data are essential in developing, testing, and ensuring the safety of unmanned aerial systems in operation. Alternatives to Dryden and von Kármán turbulence models are required, aimed explicitly at urban air spaces to generate turbulent wind data. We present a novel method to generate realistic wind data for the safe operation of small unmanned aerial vehicles in urban spaces. We propose a non-intrusive reduced order modeling approach to replicate realistic wind data and predict wind fields. The method uses a well-established large-eddy simulation model, the parallelized large eddy simulation model, to generate high-fidelity data. To create a reduced-order model, we utilize proper orthogonal decomposition to extract modes from the three-dimensional space and use specialized recurrent neural networks and long-term short memory for stepping in time. This paper combines the traditional approach of using computational fluid dynamic simulations to generate wind data with deep learning and reduced-order modeling techniques to devise a methodology for a non-intrusive data-based model for wind field prediction. A simplistic model of an isolated urban subspace with a single building setup in neutral atmospheric conditions is considered a test case for the demonstration of the method. 

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2. Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity

   https://doi.org/10.1016/j.rinam.2023.100430  

   Ballarin, Francesco; Lee, Sanghyun; Yi, Son-Young (February 2024, Results in Applied Mathematics)

   This paper explores an iterative approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biot’s poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess. 

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3. Physics-informed machine learning for automatic model reduction in chemical reaction networks

   https://doi.org/10.1038/s41598-025-92680-8  

   Pateras, Joseph; Zhang, Colin; Majumdar, Shriya; Pal, Ayush; Ghosh, Preetam (December 2025, Scientific Reports)

   Abstract Physics-informed machine learning bridges the gap between the high fidelity of mechanistic models and the adaptive insights of artificial intelligence. In chemical reaction network modeling, this synergy proves valuable, addressing the high computational costs of detailed mechanistic models while leveraging the predictive power of machine learning. This study applies this fusion to the biomedical challenge of A$$\beta$$fibril aggregation, a key factor in Alzheimer’s disease. Central to the research is the introduction of an automatic reaction order model reduction framework, designed to optimize reduced-order kinetic models. This framework represents a shift in model construction, automatically determining the appropriate level of detail for reaction network modeling. The proposed approach significantly improves simulation efficiency and accuracy, particularly in systems like A$$\beta$$aggregation, where precise modeling of nucleation and growth kinetics can reveal potential therapeutic targets. Additionally, the automatic model reduction technique has the potential to generalize to other network models. The methodology offers a scalable and adaptable tool for applications beyond biomedical research. Its ability to dynamically adjust model complexity based on system-specific needs ensures that models remain both computationally feasible and scientifically relevant, accommodating new data and evolving understandings of complex phenomena. 

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4. Sparse Reduced-Order Modeling of a Hovering Hawkmoth’s Wake

   https://doi.org/10.1115/FEDSM2024-130651  

   Lionetti, Seth; Hedrick, Tyson L; Li, Chengyu (July 2024, American Society of Mechanical Engineers)

   Abstract As insects fly, their wings generate complex wake structures that play a crucial role in their aerodynamic force production. This study focuses on utilizing reduced order modeling techniques to gain valuable insights into the fluid dynamic principles underlying insect flight. Specifically, we used an immersed-boundary-method-based computational fluid dynamics (CFD) solver to simulate a hovering hawkmoth’s wake, and then identified the most energetic modes of the wake using proper orthogonal decomposition (POD). Furthermore, we employed a sparse identification of nonlinear dynamics (SINDy) approach to find a simple reduced order model that relates the most energetic POD modes. Through this process, we formulated multiple different models incorporating varying numbers of POD modes. To compare the accuracy of these models, we utilized a force survey method to estimate the aerodynamic forces produced by the hawkmoth’s wings. This force survey method uses an impulse-based approach to calculate the aerodynamic lift and drag based solely on the velocity and vorticity information provided by the model. By comparing the estimated aerodynamic force with the actual force production calculated by the CFD solver, we were able to find the simplest model that still provides an accurate representation of the complex wake produced by the hovering hawkmoth wings. We also evaluated the stability and accuracy of this model as the number of flapping cycles increases with time. The reduced order modeling of insect flight has important implications for the design and control of bio-inspired micro-aerial vehicles. In addition, it holds the potential to reduce the computational cost associated with high-fidelity CFD simulations of complex flows. 

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5. A High-Accuracy, Low-Order Thermal Model of SiC MOSFET Power Modules Extracted from Finite Element Analysis via Model Order Reduction

   https://doi.org/10.1109/ECCE.2019.8912839  

   Entzminger, Cameron; Qiao, Wei; Qu, Liyan; Hudgins, Jerry L. (September 2019, 2019 IEEE Energy Conversion Congress and Exposition (ECCE))

   Silicon carbide (SiC) MOSFET power modules are being used for high power applications because of their superior thermal characteristics and high blocking voltage capabilities over traditional silicon power modules. This paper explores modeling the thermal process of a SiC MOSFET power module through a high-order finite element analysis (FEA) based thermal model and then reducing the order of the FEA thermal model using a Krylov subspace method. The low-order thermal model has a significantly reduced computation cost compared to the FEA model while preserving the accuracy of the model. The proposed method is applied to generate low-order thermal models for a SiC MOSFET, which are validated by computer simulations with respect to the FEA thermal model. 

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