Title: Global space-time low-complexity numerical methods for the time-dependent Schrödinger equation Abstract The aim of this talk is to present novel global space-time methods for the approximation of the time-dependent Schrödinger equation on low-complexity manifolds. The backbone of the approach is the use of a least-square formulation of the time-dependent…
Title: An immersed boundary method based on the resolution of an optimal control problem Abstract The numerical resolution of partial differential equations in domains with an intricate, a priori unknown or deforming over time geometry, generally induce difficulties related to mesh generation. Indeed, solving such problems requires, classically, the generation…
Title: A primer on physics-informed machine learning Abstract Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differential equation that quantifies the physical inconsistency. Practitioners often…
Title: A class of parabolic fractional reaction-diffusion systems with control of total mass: Theory and numerics Abstract: In this talk based on [1, 2], we present some new results about global-in-time existence of strong solutions to a class of fractional parabolic reaction–diffusion systems posed in a bounded open subset of…
Title: Energy consistent time discretisation of port-Hamiltonian systems Abstract Various ordinary and partial differential equations arising from physics can be written as port-Hamiltonian systems. Their Hamiltonian function represents an energy that is conserved or dissipated along solutions. Numerical schemes are energy consistent, if the Hamiltonian is preserved or dissipated also…
Title: Curved meshes for a diffusion problem with a surface Laplacian Abstract We study a diffusion problem with boundary conditions that involve a surface Laplacian. We present the numerical analysis of a high-order finite element discretization. A smooth domain is considered for the definition of this boundary operator. The discrtized…
Title: Photon tunneling heat transfer in particulate system: physical characteristics and homogenization theory Abstract Radiative transfer equation (RTE) is the commonly accepted continuum scale governing equation for radiative heat transfer in particulate system. However, its applicability is questionable for non-random, densely and regularly packed particulate systems, due to dependent scattering…
Title: Approximating partial differential equations with missing input data Abstract We consider the problem of numerically approximating the solution of partial differential equations for which not all the input data are known. A situation of particular interest is when the boundary conditions are unknown, or only partially known. To alleviate…
Title: Hilbertian degenerations Abstract We study problems involving entities to which a “mass” is attached. This quantity can actually be a mass in the usual sense for systems of particles, but it can also be a thermal capacity in the context of heat transfer, or a kind of charisma in…
Title: Towards trustworthy use of scientific machine-learning in large-scale numerical simulations Abstract Recently, scientific machine learning (SciML) has expanded the capabilities of traditional numerical approaches by simplifying computational modeling and providing cost-effective surrogates. However, SciML models suffer from the absence of explicit error control, a computationally intensive training phase, and…
