Le prochain colloquium aura lieu mercredi 12 mars. Francis Bach nous parlera de réseaux de neurones à 11h en Amphi C.

Physics-informed kernel learning

Physics-informed machine learning typically integrates physical priors into the learning process by
minimizing a loss function that includes both a data-driven term and a partial differential equation
(PDE) regularization. Building on the formulation of the problem as a kernel regression task, we
use Fourier methods to approximate the associated kernel, and propose a tractable estimator that
minimizes the physics-informed risk function. We refer to this approach as physics-informed kernel
learning (PIKL). This framework provides theoretical guarantees, enabling the quantification of the
physical prior’s impact on convergence speed. We demonstrate the numerical performance of the
PIKL estimator through simulations, both in the context of hybrid modeling and in solving PDEs.
In particular, we show that PIKL can outperform physics-informed neural networks in terms of both
accuracy and computation time. Additionally, we identify cases where PIKL surpasses traditional
PDE solvers, particularly in scenarios with noisy boundary conditions.