Transfer physics informed neural network: a new framework for distributed physics informed neural networks via parameter sharing

We introduce Transfer Physics Informed Neural Network (TPINN), a neural network-based approach for solving forward and inverse problems in nonlinear partial differential equations (PDEs). In TPINN, one or more layers of physics informed neural network (PINN) corresponding to each non-overlapping subdomains are changed using a unique set of parameters for each PINN. The remaining layers of individual PINNs are the same through parameter sharing. The subdomains can be those obtained by partitioning the global computational domain or subdomains part of the problem definition, which adds to the total computational domain. Solutions from different subdomains are connected while training using problem-specific interface conditions incorporated into the loss function. The proposed method handles forward and inverse problems where PDE formulation changes or when there is a discontinuity in PDE parameters across different subdomains efficiently. Parameter sharing reduces parameter space dimension, memory requirements, computational burden and increases accuracy. The efficacy of the proposed approach is demonstrated by solving various forward and inverse problems, including classical benchmark problems and problems involving parameter heterogeneity from the heat transfer domain. In inverse parameter estimation problems, statistical analysis of estimated parameters is performed by solving the problem independently six times. Noise analysis by varying the noise level in the input data is performed for all inverse problems.