[general_dat] [recordatorio] Coloquio especial conjunto DF-DC-DM-IC - Martin Arjovsky

[Pablo Groisman]

Hola!

Quería recordar sobre esta charla que tendrá lugar mañana y aprovechar para
destacar que tratará sobre avances recientes en uno de los problemas del
milenio. Mas información acá:
https://deepmind.google/blog/discovering-new-solutions-to-century-old-problems-in-fluid-dynamics/

Saludos!


On Fri, Dec 5, 2025 at 8:05 AM Departamento de Matematica <depto at dm.uba.ar>
wrote:

> Estimada comunidad:
>
> Queremos invitarlos a un coloquio especial conjunto de los departamentos
> de Física, Computación, Matemática y el Instituto de Cálculo a cargo de *Martín
> Arjovsky* (DeepMind).
>
> Se realizará el miércoles 10 de diciembre a las 15hs en el aula 1402 del
> 0+infinito. La charla será en castellano.
>
> Están todas/os cordialmente invitadas/os.
>
> Título: Discovery of Unstable Singularities in Partial Differential
> Equations using Machine Learning.
>
> Abstract: Whether singularities can form in fluids remains a foundational
> unanswered question in mathematics. This phenomenon occurs when solutions
> to governing equations, such as the 3D Euler equations, develop infinite
> gradients from smooth initial conditions. Historically, numerical
> approaches have primarily identified stable singularities. However, these
> are not expected to exist for key open problems, such as the boundary-free
> Euler and Navier-Stokes cases, where unstable singularities are
> hypothesized to play a crucial role. Here, we present the first systematic
> discovery of new families of unstable singularities. A stable singularity
> is a robust outcome, forming even if the initial state is slightly
> perturbed. In contrast, unstable singularities are exceptionally elusive;
> they require initial conditions tuned with infinite precision, being in a
> state of instability whereby infinitesimal perturbations immediately divert
> the solution from its blow-up trajectory. In particular, we present
> multiple new, unstable self-similar solutions for the incompressible porous
> media equation and the 3D Euler equation with boundary, revealing a simple
> empirical asymptotic formula relating the blow-up rate to the order of
> instability. Our approach combines curated machine learning architectures
> and training schemes with a high-precision Gauss-Newton optimizer,
> achieving accuracies that significantly surpass previous work across all
> discovered solutions. For specific solutions, we reach near double-float
> machine precision, attaining a level of accuracy constrained only by the
> round-off errors of the GPU hardware. This level of precision meets the
> requirements for rigorous mathematical validation via computer-assisted
> proofs. This work provides a new playbook for exploring the complex
> landscape of nonlinear partial differential equations (PDEs) and tackling
> long-standing challenges in mathematical physics.
>
> Bio: Martin Arjovsky is a Research Scientist at DeepMind. Prior to that,
> he was a postdoc in SIERRA with Francis Bach, and before a PhD student at
> New York University, advised by Léon Bottou. He is from Buenos Aires,
> Argentina and received the BSc and MSc degrees from the University of
> Buenos Aires. He also spent time in different places (including Google,
> Facebook, Microsoft, Université de Montréal, and DeepMind). His master’s
> thesis advisor was Yoshua Bengio, who also advised him during his stay at
> UdeM. In general, he’s interested in the intersection between learning and
> mathematics, how we can ground the different learning processes that are
> involved in different problems, and leverage this knowledge to develop
> better algorithms. Along these lines, he’s worked in many different areas
> of machine learning, including optimization, unsupervised learning, out of
> distribution generalization, and exploration in reinforcement learning.
> --
> Departamento de Matemática, FCEyN, UBA
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