Physics-informed Tensor-train ConvLSTM for Volumetric Velocity Forecasting of Loop Current

TL;DR

This paper introduces a novel physics-informed Tensor-train ConvLSTM model for 4D volumetric velocity forecasting of the Loop Current in the Gulf of Mexico, integrating physical laws and advanced neural network techniques.

Contribution

It develops a 4D higher-order recurrent neural network with tensor decomposition and physics-informed learning, advancing geospatial forecasting beyond existing methods.

Findings

Outperforms state-of-the-art in Loop Current velocity forecasting

Effective in capturing long-term dependencies and physical constraints

Demonstrates robustness over one-week prediction horizon

Abstract

According to the National Academies, a weekly forecast of velocity, vertical structure, and duration of the Loop Current (LC) and its eddies is critical for understanding the oceanography and ecosystem, and for mitigating outcomes of anthropogenic and natural disasters in the Gulf of Mexico (GoM). However, this forecast is a challenging problem since the LC behaviour is dominated by long-range spatial connections across multiple timescales. In this paper, we extend spatiotemporal predictive learning, showing its effectiveness beyond video prediction, to a 4D model, i.e., a novel Physics-informed Tensor-train ConvLSTM (PITT-ConvLSTM) for temporal sequences of 3D geospatial data forecasting. Specifically, we propose 1) a novel 4D higher-order recurrent neural network with empirical orthogonal function analysis to capture the hidden uncorrelated patterns of each hierarchy, 2) a convolutional tensor-train decomposition to capture higher-order space-time correlations, and 3) to incorporate prior physic knowledge that is provided from domain experts by informing the learning in latent space. The advantage of our proposed method is clear: constrained by physical laws, it simultaneously learns good representations for frame dependencies (both short-term and long-term high-level dependency) and inter-hierarchical relations within each time frame. Experiments on geospatial data collected from the GoM demonstrate that PITT-ConvLSTM outperforms the state-of-the-art methods in forecasting the volumetric velocity of the LC and its eddies for a period of over one week.