Multi-Fidelity Physics-Informed Neural Networks (PINN) with Boundary-Aware Losses for Ice-Bed Topography Prediction

Tartela Tabassum, Pavan Raj Ravi, Jianwu Wang

Keywords: Multi-fidelity learning, PINNs, boundary-aware losses, Glacier bed inversion, Ice dynamics

TL;DR: We introduce a multi-fidelity PINN framework that leverages boundary-aware losses for more accurate PDE-constrained learning tasks, demonstrated on ice-bed topography prediction.

Abstract: Predicting ice dynamics and sea-level rise requires an understanding of subglacial bedrock topography; however, inversion remains a challenging task in data-sparse regions where surface observations are limited. Some conventional machine learning methods face challenges in predicting subglacial topography due to heavy reliance on purely data correlations and cannot guarantee physical consistency, especially in data-sparse regions. Physics-Informed Neural Networks (PINNs) address this limitation by embedding partial differential equation (PDE) constraints into deep learning, enabling more physically consistent predictions. However, most existing PINN formulations depend on a single fidelity of physics, and soft boundary penalties can still compromise performance. We propose a multi-fidelity PINN framework for ice-bed topography prediction that advances beyond these limitations in two ways. First, we introduce multi-fidelity residual coupling, jointly enforcing the shallow-ice approximation (SIA) and reduced-Stokes equations within a single network. This coupling improves accuracy while maintaining physics consistency, achieving strong predictive performance (e.g., Test MSE = 0.028, and $R^2$ = 0.97). Second, we design a boundary-aware weak-form loss that supports traction/flux (Neumann) and optional Dirichlet constraints, allowing flexible enforcement of margin physics. Experiments show that hard Dirichlet enforcement over-constrains the model and reduces accuracy, while soft or selective enforcement preserves predictive quality. To our knowledge, this is the first Physics-Informed Neural Network (PINN) framework for predicting ice-bed topography that unifies multi-fidelity partial differential equation (PDE) residuals with configurable boundary-aware losses, providing a practical and extensible approach to physically plausible predictions in data-sparse regimes.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 23217