Improved Training of Physics-Informed Neural Networks with Model Ensembles

Understand

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data.

• However, training such physics-informed neural networks (PINNs) is notoriously difficult in practice since PINNs often converge to wrong solutions.
• In this paper, we address this problem by training an ensemble of PINNs.
• Our approach is motivated by the observation that individual PINN models find similar solutions in the vicinity of points with targets (e.g., observed data or initial conditions) while their solutions may substantially differ farther away from such points.