Differentiable PDE Solvers - A Shift of Paradigms for Numerical Simulations

In this talk, I will talk about lessons from the area of AI / deep learning for physics simulations with numerical solvers. A key focus is the utilization of solvers that are capable of providing gradient information, i.e. "differentiable simulations". These solvers seamlessly integrate with deep learning algorithms, presenting numerous advantages in arising from AI-based components in solvers, particularly in the context of flow simulations. However, the availability of gradient computation is not ubiquitous in many existing simulation environments. Avenues for computing them will be discussed, as well as fallbacks if they're not available (yet). I will show how to leverage differentiable solvers in varied applications such as closure modeling for Navier-Stokes, accelerated solving and inverse problems.