Continuous PDE Dynamics Forecasting with Neural Fields

Topic: Continuous PDE Dynamics Forecasting with Neural Fields

Abstract:

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE’s flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

Speaker(s):

Matthieu Kirchmeyer is a final-year PhD student at Sorbonne Université (graduating in spring 2023) advised by Patrick Gallinari and Alain Rakotomamonjy. He is also an ML researcher at Criteo AI Lab. He develops deep learning models which generalize to out-of-distribution data for spatio-temporal dynamics forecasting e.g., in science and classification problems e.g., in computer vision. Previously, he obtained his Master’s degree at Mines Paris - PSL and at Ecole Normale Supérieure Paris Saclay (Master MVA).

Yuan Yin is a 3rd-year PhD student in MLIA Team at ISIR - Sorbonne University supervised by Patrick Gallinari and Nicolas Baskiotis, Sorbonne University. His research focuses on machine learning and deep learning for spatio-temporal sequence modeling, prediction, and analysis of complex stochastic behaviour. He recieved his BSc in Computer Science from Beihang University in 2016, and MSc in Computer Science from Paris Cité University (1st year) and Sorbonne University (2nd year) in 2019.