FAU MoD Course: Discovery of singularities with physics-informed neural networks

Date: Wed. – Fri. December 2 – 4, 2026
Event: FAU MoD Course
Organizer: FAU MoD, Research Center for Mathematics of Data at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg

FAU MoD Course: Discovery of singularities with physics-informed neural networks
Speaker: Prof. Dr. Gonzalo Cao-Labora
Affiliation: EPFL, École Polytechnique Fédérale de Lausanne

Abstract. The course will be concerned with recent strategies to rigorously prove self-similar singularity formation, where the candidate for the singularity is obtained via physics-informed neural networks (PINNs). This is one of the strategies currently being considered to tackle the major open problems in the analysis of fluids, such as singularity formation for incompressible Euler or for Navier–Stokes, the latter being the Clay Millennium Prize problem.
We will start by understanding the techniques in the simpler setting of the self-similar Burgers shock. Burgers is a 1-D model for compressible fluids that reflects the overall strategy while simplifying certain parts of the arguments due to being 1-D and local. Then, we will talk about the neural-network techniques and the mathematical reformulations of the problem that are useful in this context, in order to find a candidate for a self-similar singularity for fluids equations. Finally, we will explain how one can obtain a rigorous proof from such a candidate, which is intimately related to the question of the stability of these solutions and to the problem of turning an inviscid singularity into a viscous one.

BIO.- Gonzalo Cao-Labora did his BSc at UPC (Barcelona) under the double-degree CFIS program, completing his last year at Princeton University. Then, he obtained his PhD from the MIT – Massachusetts Institute of Technology in 2024. After having postdoctoral positions at the Courant Institute – New York University, he is currently at the École Polytechnique Fédérale de Lausanne, Switzerland.

His research touches different areas in PDE, such as Dispersive Equations, Elliptic Overdetermined Problems and Analysis of Fluids, where he studies aspects such as self-similar singularity formation, stability of singularities, and stability of vortices. Some of his recent research involves a more geometric flavour such as Schiffer-type problems or the existence of Einstein metrics.

Prof. Cao-Labora’s research benefits from the interaction of analytical arguments, computer-assisted proofs, and numerics. Recently, he has been involved in collaborating with other academics and machine learning experts from Google DeepMind in order to use neural networks (specifically, physics-informed neural networks, or PINNs) to discover new singularities. Those numerical discoveries can then be upgraded to rigourous mathematical singularities, combining computer-assistance and analytical arguments.

He has received the 2025 R. E. Moore Award and the 2026 Vicent Caselles Prize for his PhD thesis, awarded by the Spanish Mathematical Society and the BBVA Foundation.

AUDIENCE

This is a hybrid event (on-site/online) designed for advanced master’s students and beyond, focusing on in-depth discussions and technical insights.
Open to: Public, Students, Postdocs, Professors, Faculty, Alumni and the scientific community all around the world.

WHEN

Wed. – Fri. December 2 – 4, 2026
Time-table: TBA

WHERE

On-site / Online

[On-site] FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg
Cauerstraße 7/9, 91058 Erlangen, Bavaria (Germany)
Felix-Klein building. Mathematik/Informatik
How to get to Erlangen?

[Online] https://www.fau.tv/clip/id/63064

Short-link to share this event: https://go.fau.de/1ea-c

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FAU MoD Course: Discovery of singularities with physics-informed neural networks

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