Computational Physics and Machine Learning
Simulating physical systems with deep leaning
Deep learning-based methods have shown promising results for simulating complex physical systems, often reducing the computational burden of traditional solvers by leveraging the low dimensionality inherent to many dynamical systems. These methods will be studied in the context of climate modelling and turbulence, with the aim of simulating large volumes of data over long periods of time, such as the dynamics of subglacial lakes, at a reduced computational cost. We will also explore the theoretical underpinnings of these methods, studying how low-dimensionality is exploited, and how physical symmetries can be incorporated (e.g., equivariance).
Machine learning for prediction of complex physical systems
Joint works are done with Team Fluid Dynamics, Environment, Climate to use AI for scientific questions related to complex physical systems. One such example is the prediction of climate extreme events, specifically heatwaves in climate, using DL-based methods. To estimate the probabilities of occurrence of the event (depending on the initial state), in practice using data from climate models, we proposed a machine learning approach by tailoring neural networks, and tested its performance on heat wave prediction. The method integrates learning and physical knowledge about the phenomena, using the peculiar situation in climate modeling where one has a large number of (digital) observation while remaining a data-poor regime. To address the lack of data issue, we suggested two strategies: one based on a simple assumption about the joint statistics of predictors and predictand (a Gaussian model), which was shown to be competitive with the more sophisticated neural network for heat wave prediction, even outperforming it when data is scarce