One-dimensional ice shelf hardness inversion: Clustering behavior and collocation resampling in physics-informed neural networks

Abstract

We investigate the use of Physics-Informed Neural Networks (PINNs) for ice shelf hardness inversion. PINNs were trained to invert for ice shelf hardness (B) profiles using synthetic datasets of one-dimensional (1D) ice shelf velocity (u) and thickness (h) contaminated by noise, with no training data provided for B. A hyperparameter γ is introduced in the objective function to adjust the relative weight of the neural network fit to training data and its fit to known physical laws. When the data is contaminated by noise, the equation loss should be weighted more heavily than the data loss to de-noise the predictions. However, we observe that PINN predictive performance is highly unreliable when γ is large. The prediction errors are distributed bimodally, with one cluster corresponding to accurate, “low-error” solutions, and the other consisting of “high-error” solutions that fit poorly to the ground truth datasets. The high-error PINN solutions are associated with the failure of the PINN to correctly learn the velocity spatial gradients that appear in the governing equations. We employ an alternative algorithm to improve the PINN inversion accuracy, which we call collocation resampling: the PINN is initially trained for a small number of iterations for which the collocation points for evaluating the equation loss are randomly resampled after each iteration; then, a fixed set of collocation points are used. This approach achieves predictive accuracies comparable to those attained by low-error solutions for the original training scheme with γ1−γ≫1, but with no clustering and minimal computational cost.