CMX Lunch Seminar

Many fundamental problems on probability measure spaces, including optimal transport, mean-field control/games, and Wasserstein gradient flows, are computationally demanding. Existing learning methods often rely on solvers designed for individual problem instances and require costly retraining for each new instance. In-context learning with transformers offers a new paradigm for approximating families of operators from only a few context examples, without task-specific retraining. In this talk, I will present our recent work on a self-supervised in-context operator learning framework for approximating solution operators on probability measure spaces. The framework is independent of discretization, making it well suited to high-dimensional measure transport problems, and requires no supervised solution labels, substantially reducing data-generation costs. I will demonstrate its applications to optimal transport, mean-field control, swarm control, Wasserstein gradient flows, as well as score matching. I will also some our recent analysis of the proposed transformer model, connecting our results to the emerging theory of in-context learning and highlighting their broader theoretical implications.