Plenary Talks

Topic (provisional): Optimization and statistics for physics-informed machine learning

Topic (provisional): Boundary element methods for wave propagation problems

Topic (provisional): Cryptographic algorithms and protocols

Topic (provisional): Greedy optimal sampling for solar inverse problems

Title: "How to preserve multi-dimensional equilibria for hyperbolic balance laws"

Abstract: Many conservation and balance laws admit families of moving steady states that are crucial to preserve at the numerical level. While several techniques have been developed to achieve this in one dimension, few are available for multidimensional problems, and those often apply only to linear cases. The so-called Global Flux (GF) approach [Chertock, et al. 2018] integrates multiple terms into a single physical flux, yielding a unified differential operator acting on a more complex flux function. We extend this to multiple dimensions [Barsukow, et al. 2025, Barsukow, et al. 2026] both in finite element and finite volume formulations, in order to discretely preserve truly multi-dimensional equilibria as divergence free solutions. While natively defined on Cartesian grids, we also present a smooth extension to curvilinear domains using a ghost-point boundary extrapolation method.

Topic (provisional): Geometrical and topological aspects of deep learning