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Neural Networks Learn to Speed Up Simulations


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Credit: Golden Wind

Physical scientists and engineering research and development (R&D) teams are embracing neural networks in attempts to accelerate their simulations. From quantum mechanics to the prediction of blood flow in the body, numerous teams have reported on speedups in simulation by swapping conventional finite-element solvers for models trained on various combinations of experimental and synthetic data.

At the company's technology conference in November, Animashree Anandkumar, Nvidia's director of machine learning research and Bren Professor of Computing at the California Institute of Technology, pointed to one project the company worked on for weather forecasting. She claimed the neural network that team created could achieve results 100,000 times faster than a simulation that used traditional numerical methods to solve the partial differential equations (PDEs) on which the model relies.


Comments


Anima Anandkumar

Thank you for writing about this important topic where there has been exciting progress. I appreciate you quoting my talk where I presented our recent work FourCastNet which enables fast and accurate weather prediction. This is enabled by the Fourier neural operator, a data-driven method to learn the underlying solution operator of the PDE. Unlike PINNs which solve one instance of the PDE, neural operators learn the solution operator that can solve for any instance in the family in a grid-free manner. This means that we do not require FNO to be retrained for different resolutions. We combine the data-driven approach of the Fourier neural operator with physics constraints to obtain the physics-informed neural operator that overcomes the challenges of optimization in PINN. I am surprised that this line of works is not quoted in the article. Please add this information: [1] Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, Pedram Hassanzadeh, Karthik Kashinath, Animashree Anandkumar "FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators" ArXiv 2022. [2] Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar "Fourier Neural Operator for Parametric Partial Differential Equations" International Conference on Learning Representations (ICLR) 2021 [3] Zongyi Li, Hongkai Zheng, Nikola Kovachki, David Jin, Haoxuan Chen, Burigede Liu, Kamyar Azizzadenesheli, Anima Anandkumar "Physics-Informed Neural Operator for Learning Partial Differential Equations" ArXiv, 2021.


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