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

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #225

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.

Author Information

Oussama Boussif (Mila)
Yoshua Bengio (Mila / U. Montreal)

Yoshua Bengio is Full Professor in the computer science and operations research department at U. Montreal, scientific director and founder of Mila and of IVADO, Turing Award 2018 recipient, Canada Research Chair in Statistical Learning Algorithms, as well as a Canada AI CIFAR Chair. He pioneered deep learning and has been getting the most citations per day in 2018 among all computer scientists, worldwide. He is an officer of the Order of Canada, member of the Royal Society of Canada, was awarded the Killam Prize, the Marie-Victorin Prize and the Radio-Canada Scientist of the year in 2017, and he is a member of the NeurIPS advisory board and co-founder of the ICLR conference, as well as program director of the CIFAR program on Learning in Machines and Brains. His goal is to contribute to uncover the principles giving rise to intelligence through learning, as well as favour the development of AI for the benefit of all.

Loubna Benabbou (University of Quebec UQAR)

Dr. Loubna BENABBOU is a Professor at the Université du Québec à Rimouski (UQAR). She is an industrial engineer from EMI Engineering School and holder of MBA and PhD in machine learning and optimization from Laval University. Her research work lies to machine learning theory and mathematical optimization in general. She is interested in improving the generalization capacity of multi-class classifiers using statistical learning theory and mathematical optimization. She is also interested to develop and to apply machine learning and optimization models to valorize data for making better decisions and improving operational processes in finance, supply chain management, healthcare and energy.

Dan Assouline (Mila)

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