Abstract: We introduce Deep Statistical Solvers (DSS), a new class of trainable solvers for optimization problems, arising from system simulations and others. The key idea is to learn a solver that generalizes to a given distribution of problem instances. This is achieved by directly using as loss the objective function of the problem, as opposed to most previous Machine Learning based approaches, which mimic the solutions attained by an existing solver. Though both types of approaches outperform classical solvers with respect to speed for a given accuracy, a distinctive advantage of DSS is that they can be trained without a training set of sample solutions. Focusing on use cases of systems of interacting and interchangeable entities (e.g. molecular dynamics, power systems, discretized PDEs), the proposed approach is instantiated within a class of Graph Neural Networks. We experimentally validate the approach on large linear problems, and on non-linear AC power grid simulations.
Speakers: Balthazar Donon
Bio : Balthazar Donon is a PhD student at Université Paris-Saclay under the supervision of Isabelle Guyon, Marc Schoenauer and Rémy Clément. He graduated from the École polytechnique and Stanford University. He has a strong interest in the Energy domain and its environmental and societal implications, as well as in Artificial Intelligence. He is currently pursuing his PhD in Computer Science at RTE (French transmission system operator) and Université Paris-Sud, and aims at developing novel artificial neural network algorithms targeted at Power System applications.
Affiliation: Université Paris-Saclay