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Conference Papers Year : 2020

Deep Statistical Solvers

Wenzhuo Liu
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  • PersonId : 1079812
Antoine Marot
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  • PersonId : 1079813
Zhengying Liu
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  • PersonId : 1038060
Marc Schoenauer


This paper introduces 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. Under sufficient conditions, we prove that the corresponding set of functions contains approximations to any arbitrary precision of the actual solution of the optimization problem. The proposed approach is experimentally validated on large linear problems, on demonstrating super-generalisation properties; And on AC power grid simulations, on which the predictions of the trained model have a correlation higher than 99.99% with the outputs of the classical Newton-Raphson method (known for its accuracy), while being 2 to 3 orders of magnitude faster.
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Dates and versions

hal-02974541 , version 1 (23-10-2020)
hal-02974541 , version 2 (26-10-2020)
hal-02974541 , version 3 (02-12-2020)


  • HAL Id : hal-02974541 , version 3


Balthazar Donon, Wenzhuo Liu, Antoine Marot, Zhengying Liu, Isabelle Guyon, et al.. Deep Statistical Solvers. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems, Dec 2020, Vancouver / Virtuel, Canada. ⟨hal-02974541v3⟩
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