Nonlinear Model
Nonlinear models are mathematical representations of systems where the output is not directly proportional to the input, capturing complex relationships prevalent in numerous scientific domains. Current research emphasizes developing and improving nonlinear model architectures, including neural networks (e.g., autoencoders, GANs), Volterra series, and Koopman operator methods, often incorporating techniques like adaptive sampling and Bayesian inference to enhance efficiency and robustness. These advancements are crucial for addressing challenges in diverse fields such as structural health monitoring, control systems, and machine learning, enabling more accurate predictions and improved decision-making in complex systems.
Papers
Stability-Certified Learning of Control Systems with Quadratic Nonlinearities
Igor Pontes Duff, Pawan Goyal, Peter Benner
SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study
Aurelio Raffa Ugolini, Valentina Breschi, Andrea Manzoni, Mara Tanelli
Nonlinear Sheaf Diffusion in Graph Neural Networks
Olga Zaghen