Physics-Informed Neural Network with Variable Initial Conditions

Abstract

This work addresses an extension of Physics-Informed Neural Network (PINN), which learns solutions of partial differential equations (PDE). In the originally proposed PINN [1], the initial conditions are kept constant. In this study, we extend the PINN so that the initial conditions can be varied by means of low-dimensional identifiers which represent the initial conditions. A validity of the proposed method is confirmed through the PDE for the liquid film flow. The solutions of the PDE predicted by the PINN showed good agreement with those obtained by the finite difference method, and the dependence of the initial conditions are also correctly reproduced. As requirements for the low-dimensional identifier of the initial conditions, it is suggested that continuity and uniqueness are necessary condition and the linearity is sufficient condition.