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Neuro-Symbolic Partial Differential Equation Solver
Pouria Akbari Mistani · Samira Pakravan · Rajesh Ilango · Sanjay Choudhry · Frederic Gibou

We present a highly scalable strategy for developing mesh-free neuro-symbolic partial differential equation solvers from existing numerical discretizations found in scientific computing. This strategy is unique in that it can be used to efficiently train neural network surrogate models for the solution functions and the differential operators, while retaining the accuracy and convergence properties of state-of-the-art numerical solvers. This neural bootstrapping method is based on minimizing residuals of discretized differential systems on a set of random collocation points with respect to the trainable parameters of the neural network, achieving unprecedented resolution and optimal scaling for solving physical and biological systems.

Author Information

Pouria Akbari Mistani (NVIDIA)
Pouria Akbari Mistani

Pouria received his PhD in Mechanical Engineering with an emphasis in Computational Science and Engineering (CSE) from University of California Santa Barbara in 2020, and his MS degree in Physics with an emphasis in computational astrophysics from University of California Riverside in 2014. Prior to that, he received two B.S. degrees in Aerospace Engineering and Physics from Sharif University of Technology in Iran in 2013. Pouria did his postdoctoral studies at Merck Research Lab, where he developed computational models for high concentration biotherapeutic formulations. Pouria’s research interest is focused on computational modeling and simulation of multiscale phenomena. In his career he has applied advanced numerical techniques to develop computational models and HPC simulation softwares for several complex physical systems including galaxy clusters, cell aggregates, atomic islands, instabilities of high concentration protein formulations, parametrization of molecular dynamics force fields, and using AI for accelerating molecular dynamics simulations.

Samira Pakravan (UCSB)
Rajesh Ilango (NVIDIA)
Sanjay Choudhry (NVIDIA)
Frederic Gibou (University of California Santa Barbara)

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