Dynamical System
Dynamical systems theory focuses on understanding the evolution of systems over time, aiming to predict future states and uncover underlying mechanisms. Current research emphasizes developing data-driven models, employing architectures like recurrent neural networks, transformers, and physics-informed neural networks, often coupled with techniques from optimal transport and Koopman operator theory, to learn system dynamics from observational data, even in the presence of noise and incomplete information. This field is crucial for advancing scientific understanding across diverse disciplines, from climate modeling and neuroscience to engineering control systems and materials science, by providing robust and efficient tools for analysis, prediction, and control of complex systems. The development of more accurate and efficient methods for learning and analyzing dynamical systems from limited and noisy data remains a key focus.
Papers
Response Theory via Generative Score Modeling
Ludovico Theo Giorgini, Katherine Deck, Tobias Bischoff, Andre Souza
LLMs learn governing principles of dynamical systems, revealing an in-context neural scaling law
Toni J.B. Liu, Nicolas Boullé, Raphaël Sarfati, Christopher J. Earls
Control-Theoretic Techniques for Online Adaptation of Deep Neural Networks in Dynamical Systems
Jacob G. Elkins, Farbod Fahimi
AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression
Mario De Florio, Ioannis G. Kevrekidis, George Em Karniadakis
Forecasting Fold Bifurcations through Physics-Informed Convolutional Neural Networks
Giuseppe Habib, Ádám Horváth