Atmosphere Ocean Science Friday Seminar

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Constrained Deep Generative Modeling

Speaker: Matthieu Blanke

Location: Warren Weaver Hall 1314

Date: Friday, November 21, 2025, 4 p.m.

Synopsis:

Generative deep learning methods have become powerful tools for modeling complex physical data distributions with uncertainty. While they produce perceptually convincing samples in imaging tasks, many scientific applications in climate sciences require outputs to satisfy strict mathematical constraints, such as conservation laws or dynamical equations. Enforcing such constraints at sampling time, especially in a zero-shot setting without retraining, is therefore critical for physically consistent predictions. In this talk, we present a mathematical framework for constrained sampling based on the variational formulation of Langevin dynamics, and duality in Wasserstein space. Building on this foundation, we introduce Split Augmented Lagrangian Langevin, a primal-dual sampling algorithm that progressively enforces constraints via variable splitting, with convergence guarantees. We demonstrate its effectiveness on physically constrained generative modeling tasks. Applications include energy-conserving diffusion models for data assimilation and inverse problems