Quadratic Model

Quadratic models are increasingly used to represent dynamical systems, offering a balance between model complexity and computational tractability. Current research focuses on developing methods to learn these models from data, particularly using operator inference techniques, while ensuring stability properties crucial for reliable predictions. This approach finds applications in diverse fields, including process engineering (e.g., modeling chemical reactions) and the analysis of neural network behavior, contributing to improved digital twin architectures and a deeper understanding of complex systems. The ability to guarantee stability and efficiently learn these models from data is driving significant advancements.

Papers

February 27, 2024

Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference
Ion Victor Gosea, Luisa Peterson, Pawan Goyal, Jens Bremer, Kai Sundmacher, Peter Benner
Dynamical System Reduced Order Data Driven Reduced Order Operator Inference Quadratic Model

August 26, 2023

Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference
Pawan Goyal, Igor Pontes Duff, Peter Benner
Financial Application Dynamical System Dynamical Model Weak Sindy Operator Inference Quadratic Model

May 24, 2022

Quadratic models for understanding catapult dynamics of neural networks
Libin Zhu, Chaoyue Liu, Adityanarayanan Radhakrishnan, Mikhail Belkin
Neural Network Wide Neural Network Large Learning Rate Quadratic Neural Network Quadratic Model

Quadratic Model

Papers

Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference

Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference

Quadratic models for understanding catapult dynamics of neural networks