M²F-PINN: A Multi-Scale Frequency-Domain Multi-Physics-Informed Neural Network for Ocean Forecasting

ICLR 2026 Conference Submission19568 Authors

Keywords: physics-informed neural networks(PINN), multi-scale Fourier feature, ocean forecasting

TL;DR: This work introduces a multi-scale, frequency-domain, physics-informed neural network for ocean forecasting that enhances physical interpretability and effectively captures frequency information.

Abstract: Physics‐informed neural networks (PINNs) embed physical laws into data-driven learning and are becoming increasingly influential in climate and ocean forecasting. Yet effectively capturing multi-scale variability across high and low frequencies while maintaining training stablility and ensuring convergence remains challenging for conventional PINNs. We introduce M$^2$F-PINN, a novel Transformer-based multi-scale frequency-domain multi-PINN algorithm designed to 1) mitigate spectral bias via Fourier representation learning, and 2) analyze multi-scale characteristics through frequency-domain modeling, and 3) incorporate physics priors using multiple PINNs. M$^2$F-PINN leverages multi-scale Fourier networks to learn spectral components and multi-scale interactions, and employs a 3D Swin Transformer in an autoregressive setting to capture spatiotemporal regularities. The advantages of M$^2$F-PINN include: 1) adaptively learns frequency components multi-scales to improve multi-scale dynamics; 2) jointly estimates physical coefficients within the PINN modules, refining representations of physical processes; 3) preserves the Transformer framework, enabling compatibility with diverse architectures and structural decoupling; 4) extensive experiments on real-world ocean datasets show that M$^2$F-PINN outperforms deep-learning baselines and competitive ocean models (e.g., XiHe, WenHai) in predicting ocean current fields, achieving superior performance across multiple time horizons.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 19568