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 such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters as this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $1000\times$ reduction in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs.
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
Max Planck Institute for Dynamics of Complex Technical Systems（马克斯·普朗克复杂技术系统动力学研究所）；University of California San Diego（加利福尼亚大学圣地亚哥分校）；New York University（纽约大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）
Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）
Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques
Cornell University（康奈尔大学）；Catholic University of the Sacred Heart（圣心天主教大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Sandia National Laboratories（桑迪亚国家实验室）
Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation
Argonne Leadership Computing Facility（阿贡领导力计算设施）；Argonne National Laboratory（阿贡国家实验室）；The Alan Turing Institute（艾伦·图灵研究所）；Imperial College London（帝国理工学院）
Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation
TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
University of Massachusetts Dartmouth（马萨诸塞大学达特茅斯分校）；Shanghai Jiao Tong University（上海交通大学）；University of Utah（犹他大学）；Scientific Computing and Imaging Institute（科学计算与成像研究所）
