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Physics-informed Tensor-train ConvLSTM for Volumetric Velocity Forecasting

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Document pages: 11 pages

Abstract: According to the National Academies, a weekly forecast of velocity, verticalstructure, and duration of the Loop Current (LC) and its eddies is critical forunderstanding the oceanography and ecosystem, and for mitigating outcomes ofanthropogenic and natural disasters in the Gulf of Mexico (GoM). However, thisforecast is a challenging problem since the LC behaviour is dominated bylong-range spatial connections across multiple timescales. In this paper, weextend spatiotemporal predictive learning, showing its effectiveness beyondvideo prediction, to a 4D model, i.e., a novel Physics-informed Tensor-trainConvLSTM (PITT-ConvLSTM) for temporal sequences of 3D geospatial dataforecasting. Specifically, we propose 1) a novel 4D higher-order recurrentneural network with empirical orthogonal function analysis to capture thehidden uncorrelated patterns of each hierarchy, 2) a convolutional tensor-traindecomposition to capture higher-order space-time correlations, and 3) toincorporate prior physic knowledge that is provided from domain experts byinforming the learning in latent space. The advantage of our proposed method isclear: constrained by physical laws, it simultaneously learns goodrepresentations for frame dependencies (both short-term and long-termhigh-level dependency) and inter-hierarchical relations within each time frame.Experiments on geospatial data collected from the GoM demonstrate thatPITT-ConvLSTM outperforms the state-of-the-art methods in forecasting thevolumetric velocity of the LC and its eddies for a period of over one week.

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