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MAgNet: Mesh Agnostic Neural PDE Solver
Oussama Boussif · Yoshua Bengio · Loubna Benabbou · Dan Assouline

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Event URL: https://openreview.net/forum?id=tbIJmAdqYc8 »

The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. When it comes to climate predictions, fine spatio-temporal resolutions are required 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, climate modelers solve these 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.

Author Information

Oussama Boussif (Mila, Quebec AI Institute)
Oussama Boussif

I am currently a visiting research student at Mila working with Professors Yoshua Bengio and Loubna Benabbou on Machine Learning Applied to Physics. Prior to this, I obtained my engineering degree in Applied Mathematics and Data Science from CentraleSupélec (2021) and a Msc. in “Mathematics, Vision & Learning” (2021) from ENS Paris-Saclay (commonly known as MVA). I am interested in discovering physical laws and processes in a data-driven way. I am also interested in finding physically informed algorithms for scientific applications such as material discovery.

Yoshua Bengio (Mila - Quebec AI Institute)
Loubna Benabbou (University of Quebec UQAR)
Dan Assouline (Mila, Université de Montréal)

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