Large Data Solutions to 1-D Hyperbolic Systems, Ill-Posedness, and Convex Integration

Date: Mon. July 10, 2023 at 14:00H

Organized by: FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Title: Large Data Solutions to 1-D Hyperbolic Systems, Ill-Posedness, and Convex Integration

Speaker: Dr. Sam Krupa
Affiliation: Max Planck Institute for Mathematics in the Sciences (Leipzig)

Abstract.This talk focuses on the possibilities that arise from recent advances in the area of deep learning for physical simulations. In particular, it will focus on differentiable physics solvers from the larger field of differentiable programming. These solvers provide crucial information for deep learning tasks in the form of gradients, which are especially important for time-dependent processes. Also, existing numerical methods for efficient solvers can be leveraged within learning tasks. This paves the way for hybrid solvers in which traditional methods work alongside pre-trained neural network components. The resulting improvements will be illustrated with examples such as wake flows and turbulence mixing layer cases. From a machine learning perspective, regression problems with physics solvers are a highly interesting class of problems. I will conclude the talk by outlining avenues for probabilistic learning algorithms that leverage recent advance from diffusion models.


On-site / Online

[On-site] Room 01.382.Department Mathematik.
FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg.
Cauerstraße 11, 91058 Erlangen.
GPS-Koord. Raum: 49.574043N, 11.030950E

[Online] Zoom meeting link
Meeting ID: 614 4658 1599 | PIN code: 914397


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