ANR MELISSA

Partners:

• LabHC (UJM, CNRS)
• ISIR (Sorbonne Univ., CNRS)
• MAGNET (INRIA, Lille Univ.)

“The underlying dynamics ofmany physical problems are governed by parameterized partial differential equations (PDEs). Despite important scientific advances in numerical simulation, solving efficiently PDEs remains complex and often prohibitively expensive. Physics-informedMachine Learning (PiML) has recently emerged as a promising way to learn efficient surrogate solvers, and augment the physical laws by leveraging knowledge extracted from data. Despite indisputable advances, several open problems remain to be addressed in PIML: (i) Deriving generalization guarantees; (ii) Learning with a limited amount of data; (iii) Augmenting partially known physical laws; (v)Modeling uncertainty; (vi) Building foundation models for physics. MELISSA will deal with these problems from both theoretical and algorithmic perspectives. The objective is to design the next generation of provably accurate PIML algorithms in the challenging context of laser-matter interaction where data is scarce and the available physical laws only partially explain the observed dynamics.”