Physics-Informed Machine Learning under Climate Domain Shift: PDE-Free Physics Regularisation for Cloud Prediction

ICLR 2026 Conference Submission18819 Authors

Keywords: physics-in-the-loss, PDE-free physics regularization, Clausius–Clapeyron constraint, cloud (cloud fraction) prediction, out-of-distribution generalization, climate domain shift, geophysical machine learning, atmospheric thermodynamics, ERA5 reanalysis, gradient supervision (temperature sensitivity), area-weighted RMSE, physics-guided inductive bias, Physics Informed Machine Learning, Physics Informed Neural Networks

TL;DR: TL;DR: A lightweight, PDE-free physics-in-the-loss (Clausius–Clapeyron) regulariser on temperature sensitivity makes an MLP generalise better for cloud fraction under domain shift—without hurting in-distribution accuracy.

Abstract: We study out‑of‑distribution generalisation in geophysical prediction and propose CC‑PINN, a physics‑informed multi-layer perceptron (MLP) that encodes the Clausius–Clapeyron thermodynamic relation as a gradient‑based regularisation term. Unlike prior PINNs, CC-PINN requires no explicit governing-equation. CC‑PINN introduces a lightweight constraint on humidity-temperature consistency without altering network architecture. Trained on atmospheric reanalysis data (temperature, pressure, relative humidity, specific humidity, vertical velocity) using modest computational resources, CC-PINN matches a capacity-matched MLP in-distribution and improves out-of-distribution performance. CC‑PINN achieves a 12.3\% reduction in global area-weighted RMSE over a capacity‑matched MLP baseline. Under a stringent covariate-shift test - training only on the polar latitudes - CC‑PINN reduces tropical area-weighted root mean squared error (RMSE) by 22.6\% relative to the baseline, while maintaining in‑distribution parity. Ablations show the performance gains are substantially attenuated when the physics term is removed, highlighting the role of targeted domain knowledge inclusion in improving extrapolation. These findings suggest that compact, domain‑motivated regularisation can deliver robust generalisation in scientific ML tasks.

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

Submission Number: 18819