Physics-informed neural networks: A deep learaning framework for solving forward and inverse problems involving nonlinear partial differential equations. M. Raissi, P. Perdikaris, G.E. Karniadakis. Journal of Computational Physics 378 (2019) 686-707
The problem: “There exists a vast amount of prior knowledge that is currently not being utilized in modern machine learning practice. Let it be the principled physical laws that govern the time-dependent dynamics of a system, or some empirically validated rules of other domain expertise, this prior information can act as a regularization agent that constrains the space of admissible solutions to a manageable size”.
Possible solution: Gaussian process regression.
Another possible solution: Leveraging the universal function approximation of deep neural networks. The authors “expolit recent developments in automatic differentiation - one of the most useful but perhaps under-utilized techniques in scientific computing - to differentiate neural networks with respect to their input coordinates and model parameters to obtain physics-informed neural networks.