Computer Science > Machine Learning
[Submitted on 17 Jan 2024 (v1), last revised 20 Feb 2024 (this version, v3)]
Title:Space and Time Continuous Physics Simulation From Partial Observations
View PDF HTML (experimental)Abstract:Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.
Submission history
From: Steeven Janny [view email][v1] Wed, 17 Jan 2024 13:24:04 UTC (23,222 KB)
[v2] Sun, 18 Feb 2024 09:24:37 UTC (23,222 KB)
[v3] Tue, 20 Feb 2024 06:31:47 UTC (23,222 KB)
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