Deep learning has made significant progress in various fields and has emerged as a promising tool for modeling physical dynamical phenomena that exhibit highly nonlinear relationships. However, existing approaches are limited in their ability to make physically sound predictions due to the lack of prior knowledge and to handle real-world scenarios where data comes from multiple dynamics or is irregularly distributed in time and space. This thesis aims to overcome these limitations in the following directions: improving neural network-based dynamics modeling by leveraging physical models through hybrid modeling; extending the generalization power of dynamics models by learning commonalities from data of different dynamics to extrapolate to unseen systems; and handling free-form data and continuously predicting phenomena in time and space through continuous modeling. We highlight the versatility of deep learning techniques, and the proposed directions show promise for improving their accuracy and generalization power, paving the way for future research in new applications.
Short bio: Yuan Yin currently serves as a Postdoctoral Researcher within the MLIA Team at ISIR, Sorbonne University, specializing in machine learning for spatiotemporal sequence modeling and prediction, with a focus on physical dynamical systems. He successfully defended his PhD thesis in June 2023 at Sorbonne University under the supervision of Professor Patrick Gallinari and Associate Professor Nicolas Baskiotis. Yuan Yin earned his BSc in Computer Science from Beihang University in 2016 and his MSc in Computer Science from Paris Cité University and Sorbonne University in 2019.