Meta-learning PINN loss functions

Understand

We propose a meta-learning technique for offline discovery of physics-informed neural network (PINN) loss functions.

• We extend earlier works on meta-learning, and develop a gradient-based meta-learning algorithm for addressing diverse task distributions based on parametrized partial differential equations (PDEs) that are solved with PINNs.
• Furthermore, based on new theory we identify two desirable properties of meta-learned losses in PINN problems, which we enforce by proposing a new regularization method or using a specific parametrization of the loss function.
• In the computational examples, the meta-learned losses are employed at test time for addressing regression and PDE task distributions.