MAgNet: Mesh Agnostic Neural PDE SolverDownload PDF

Published: 31 Oct 2022, 18:00, Last Modified: 13 Jan 2023, 20:28NeurIPS 2022 AcceptReaders: Everyone
Keywords: physical simulations, implicit neural representations, graph neural networks, learned simulators
TL;DR: We propose a novel mesh-agnostic architecture that predicts solutions to PDE at any spatially continuous point of the PDE domain and generalizes across different meshes and resolutions.
Abstract: The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal resolutions to resolve all turbulent scales in the fluid simulations. This makes the task of accurately resolving these scales computationally out of reach even with modern supercomputers. As a result, current numerical modelers solve PDEs on grids that are too coarse (3km to 200km on each side), which hinders the accuracy and usefulness of the predictions. In this paper, we leverage the recent advances in Implicit Neural Representations (INR) to design a novel architecture that predicts the spatially continuous solution of a PDE given a spatial position query. By augmenting coordinate-based architectures with Graph Neural Networks (GNN), we enable zero-shot generalization to new non-uniform meshes and long-term predictions up to 250 frames ahead that are physically consistent. Our Mesh Agnostic Neural PDE Solver (MAgNet) is able to make accurate predictions across a variety of PDE simulation datasets and compares favorably with existing baselines. Moreover, our model generalizes well to different meshes and resolutions up to four times those trained on.
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