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Reduced-order models of flame dynamics can be used to predict and mitigate the emergence of thermoacoustic oscillations in the design of gas turbine and rocket engines. This process is hindered by the fact that these models, although often…

Fluid Dynamics · Physics 2020-07-07 Hans Yu , Matthew P. Juniper , Luca Magri

Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…

Dynamical Systems · Mathematics 2026-01-05 Yevgeniya Filanova , Igor Pontes Duff , Pawan Goyal , Peter Benner

In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To…

Numerical Analysis · Mathematics 2023-08-22 Shuhao Li , Hu Wang , Jichao Yin , Xinchao Jiang , Yaya Zhang

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…

Pattern Formation and Solitons · Physics 2025-08-12 Alessandro Alla , Rudy Geelen , Hannah Lu

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

Computational Engineering, Finance, and Science · Computer Science 2025-06-16 Shane A McQuarrie , Parisa Khodabakhshi , Karen E Willcox

Many control applications can be formulated as optimization constrained by conservation laws. Such optimization can be efficiently solved by gradient-based methods, where the gradient is obtained through the adjoint method. Traditionally,…

Optimization and Control · Mathematics 2016-05-11 Han Chen , Qiqi Wang

An alternative data-driven modeling approach has been proposed and employed to gain fundamental insights into robot motion interaction with granular terrain at certain length scales. The approach is based on an integration of dimension…

Robotics · Computer Science 2025-06-13 Guanjin Wang , Xiangxue Zhao , Shapour Azarm , Balakumar Balachandran

This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…

Optimization and Control · Mathematics 2024-08-13 Pritpal Matharu , Bartosz Protas

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…

Numerical Analysis · Mathematics 2025-03-19 Shane A. McQuarrie , Anirban Chaudhuri , Karen E. Willcox , Mengwu Guo

Reduced-order models that accurately abstract high fidelity models and enable faster simulation is vital for real-time, model-based diagnosis applications. In this paper, we outline a novel hybrid modeling approach that combines machine…

Signal Processing · Electrical Eng. & Systems 2020-03-06 Ion Matei , Johan de Kleer , Alexander Feldman , Rahul Rai , Souma Chowdhury

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

Fluid Dynamics · Physics 2020-06-10 Nirmal J. Nair , Andres Goza

We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a…

Quantum Physics · Physics 2025-05-02 Harish S. Bhat

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Numerical Analysis · Mathematics 2023-01-18 Mengwu Guo , Shane A. McQuarrie , Karen E. Willcox

For a given {\it misfit function}, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march towards a stationary point. The adjoint method, arising from…

Solar and Stellar Astrophysics · Physics 2015-05-28 Shravan Hanasoge , Aaron Birch , Laurent Gizon , Jeroen Tromp

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

Machine Learning · Computer Science 2021-06-18 Zhe Bai , Liqian Peng

In this work, we present an adjoint-based method for discovering the underlying governing partial differential equations (PDEs) given data. The idea is to consider a parameterized PDE in a general form and formulate a PDE-constrained…

Optimization and Control · Mathematics 2025-09-23 Mohsen Sadr , Tony Tohme , Kamal Youcef-Toumi

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…

Numerical Analysis · Mathematics 2026-05-25 Sean Reiter , Steffen W. R. Werner

Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper…

Systems and Control · Electrical Eng. & Systems 2023-04-14 Samuel E. Otto , Alberto Padovan , Clarence W. Rowley

This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…

Machine Learning · Computer Science 2021-03-29 Wayne Isaac Tan Uy , Benjamin Peherstorfer

Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive, meaning that they require direct access to underlying…

Dynamical Systems · Mathematics 2023-08-16 Yevgeniya Filanova , Igor Pontes Duff , Pawan Goyal , Peter Benner