Incomplete to complete multiphysics forecasting - a hybrid approach for learning unknown phenomena

Nilam Nandkishor Tathawadekar, Nguyen Anh Khoa Doan, Camilo Fernando Silva, Nils Thuerey

Keywords: neural physics simulations, multi-physics systems, reactive flows, differentiable PDE solvers

TL;DR: This paper proposes a hybrid framework that combines neural network models with an incomplete PDE solver to account for the effects of unknown physics present in the system to predict a long-term temporal evolution of a complete, multiphysics system

Abstract: Modeling complex dynamical systems where only partial knowledge of their physical mechanisms is available is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural network and data, often fail to accurately simulate the evolution of the system dynamics over a sufficiently long time and in a physically consistent manner. Therefore, we propose a hybrid approach that uses a neural network model in combination with an incomplete PDE solver that provides known but incomplete physical information. In this study, we demonstrate that the results obtained from the incomplete PDEs can be efficiently corrected at every time step by the proposed hybrid neural network – PDE solver model, so that the effect of the unknown physics present in the system is correctly accounted for. For validation purposes, the obtained simulations of the hybrid model are successfully compared against results coming from the complete set of PDEs describing the full physics of the considered system. We demonstrate the validity of the proposed approach on a reactive flow, an archetypal multi-physics system that combines fluid mechanics and chemistry, the latter being the physics considered unknown. Experiments are made on planar and Bunsen-type flames at various operating conditions. The hybrid neural network - PDE approach correctly models the flame evolution of the cases under study for significantly long time windows, yields improved generalization, and allows for larger simulation time steps.

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