Following the success of our inaugural launch event, SCAI is proud to announce its fourth seminar.

The topic of the fourth session is “Learning Physical Dynamics: From Neural Operators to World Models” – by Armand Kassaï Koupaï.

Abstract
Simulating physical systems has long relied on numerical solvers for partial differential equations, which are accurate but expensive, slow to adapt, and hard to scale to the resolutions that modern applications demand. Over the past few years, neural networks have emerged as a credible alternative: trained on simulated or observed trajectories, they learn to advance the state of a system in time at a fraction of the cost. This talk is an introduction to neural surrogates for spatio-temporal dynamics governed by PDEs. I will first (i) present the difficulties that standard neural architectures encounter on physical data, and show how they motivated the design of neural operators. Since the range of dynamical behaviors a surrogate may face is vast, I will then (ii) introduce adaptive methods, which condition the model on the dynamics at hand and yield surrogates that generalize beyond their training regime. From there I will turn to the recent wave of models pre-trained across many physical systems, often called foundation models, and (iii) argue that the world model vocabulary describes them better: they perform a single task, predicting how an environment evolves under its conditions and controls, and their strength lies in generalizing across environments rather than across tasks. I will close with the practical questions that decide how far this approach can go: scaling behavior and the availability and design of large physics datasets.

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