Nonlinear Model Reduction

Nonlinear model reduction aims to create computationally efficient approximations of complex, high-dimensional nonlinear systems, primarily focusing on reducing the computational cost of simulations and control design. Current research emphasizes data-driven approaches, employing neural networks (including autoencoders and DeepONets) and techniques like empirical interpolation methods, often combined with dimensionality reduction methods such as Proper Orthogonal Decomposition (POD) or Kernel Principal Component Analysis (KPCA), to build accurate reduced-order models. These advancements are significant for accelerating simulations in various fields, such as fluid dynamics and material science, and enabling real-time control of complex systems.

Papers

October 14, 2024

Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations
Julius Aka, Johannes Brunnemann, Jörg Eiden, Arne Speerforck, Lars Mikelsons
Latent Representation Variational Autoencoders Dimensionality Reduction Neural ODE Koopman Operator Nonlinear Model Reduction Approximation Operator

August 29, 2024

Efficient Transonic Aeroelastic Model Reduction Using Optimized Sparse Multi-Input Polynomial Functionals
Michael Candon, Maciej Balajewicz, Arturo Delgado-Gutierrez, Pier Marzocca, Earl H. Dowell
Many Sparse Reduced Order Nonlinear Model Reduction Aeroelastic Mode

June 5, 2024

Neural empirical interpolation method for nonlinear model reduction
Max Hirsch, Federico Pichi, Jan S. Hesthaven
Nonlinear Model Parabolic Partial Differential Equation Nonlinear Model Reduction Empirical Interpolation Method

March 27, 2024

Nonlinear model reduction for operator learning
Hamidreza Eivazi, Stefan Wittek, Andreas Rausch
Operator Learning Deep Operator Network Proper Orthogonal Decomposition Kernel Principal Component Analysis Model Order Reduction Nonlinear Model Reduction

March 6, 2024

TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
Yanlai Chen, Yajie Ji, Akil Narayan, Zhenli Xu
Physic Informed Neural Network PINN Method Nonlinear Model Reduction

January 19, 2024

Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning
Hao Liu, Biraj Dahal, Rongjie Lai, Wenjing Liao
Latent Variable Generalization Error Operator Learning Model Reduction Low Dimensional Structure Nonlinear Model Reduction

November 17, 2023

RONAALP: Reduced-Order Nonlinear Approximation with Active Learning Procedure
Clément Scherding, Georgios Rigas, Denis Sipp, Peter J Schmid, Taraneh Sayadi
Active Learning Reduced Order Surrogate Modeling Nonlinear Model Reduction

May 15, 2023

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
Federico Pichi, Beatriz Moya, Jan S. Hesthaven
Graph Drawing Autoencoder Architecture Graph Autoencoders Proper Orthogonal Decomposition Model Order Reduction Nonlinear Model Reduction Data Driven Model Reduction

March 16, 2023

Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductions
Jorio Cocola, John Tencer, Francesco Rizzi, Eric Parish, Patrick Blonigan
High Efficiency Surrogate Model Manifold Learning Reduced Order Dimensional Manifold Model Order Reduction Nonlinear Model Reduction

September 14, 2022

Using Spectral Submanifolds for Nonlinear Periodic Control
Florian Mahlknecht, John Irvin Alora, Shobhit Jain, Edward Schmerling, Riccardo Bonalli, George Haller, Marco Pavone
High Dimensional Nonlinear Dynamic Model Reduction Nonlinear Control Nonlinear Model Reduction

Nonlinear Model Reduction

Papers

Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations

Efficient Transonic Aeroelastic Model Reduction Using Optimized Sparse Multi-Input Polynomial Functionals

Neural empirical interpolation method for nonlinear model reduction

Nonlinear model reduction for operator learning

TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs

Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning

RONAALP: Reduced-Order Nonlinear Approximation with Active Learning Procedure

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductions

Using Spectral Submanifolds for Nonlinear Periodic Control