Effective Training of PINNs by Combining CMA-ES with Gradient Descent

Physics-Informed Neural Networks (PINNs) have recently received increasing attention, however, optimizing the loss function of PINNs is notoriously difficult, where the landscape of the loss function is often highly non-convex and rugged. Local optimization methods based on gradient information can converge quickly but are prone to being trapped in local minima for training PINNs. Evolutionary algorithms (EAs) are well known for the global search ability, which can help escape from local minima. It has been reported in the literature that EAs show some advantages over gradient-based methods in training PINNs. Inspired by the Memetic Algorithm, we combine global-search based EAs and local-search based batch gradient descent in order to make the best of both word. In addition, since the PINN loss function is composed of multiple terms, balancing these terms is also a challenging issue. Therefore, we also attempt to combine EAs with multiple-gradient descent algorithm for multi-objective optimization. Our experiments provide strong evidence for the superiority of the above algorithms.