Learning Space-Time Continuous Neural PDEs from Partially Observed States

• URL: http://arxiv.org/abs/2307.04110v2
• Date: Thu, 26 Oct 2023 10:03:26 GMT
• Title: Learning Space-Time Continuous Neural PDEs from Partially Observed States
• Authors: Valerii Iakovlev, Markus Heinonen, Harri L\"ahdesm\"aki
• Abstract summary: We introduce a grid-independent model learning partial differential equations (PDEs) from noisy and partial observations on irregular grids. We propose a space-time continuous latent neural PDE model with an efficient probabilistic framework and a novel design encoder for improved data efficiency and grid independence.
• Score: 13.01244901400942
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an efficient probabilistic framework and a novel encoder design for improved data efficiency and grid independence. The latent state dynamics are governed by a PDE model that combines the collocation method and the method of lines. We employ amortized variational inference for approximate posterior estimation and utilize a multiple shooting technique for enhanced training speed and stability. Our model demonstrates state-of-the-art performance on complex synthetic and real-world datasets, overcoming limitations of previous approaches and effectively handling partially-observed data. The proposed model outperforms recent methods, showing its potential to advance data-driven PDE modeling and enabling robust, grid-independent modeling of complex partially-observed dynamic processes.

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