Neural Solvers are neural network based solver for partial differential equations and inverse problems. Our library Neural Solvers implements the physics-informed neural network approach on scale. Physics informed neural networks allow strong scaling by design. Therefore, we have developed a framework that uses data parallelism to accelerate the training of physics informed neural networks significantly. To implement data parallelism, we use the Horovod framework, which provides near-ideal speedup on multi-GPU regimes.

The framework currently implements a variety of recent models for forward and inverse problems in natural sciences such as

• 1d Maxwell’s equation
• 1d, 2d Schrödinger’s equation
• 1d, 2d Heat equation
• 1d, 3d Wave equation

Team

• Jeyhun Rustamov
• Maksim Zhdanov
• Karan Shah (external, CASUS)

Publications

• Stiller P., Makdani V., Pöschel F. , Richard P., Debus A., Bussmann M., Hoffmann N. (2022). Continual learning autoencoder training for a particle-in-cell simulation via streaming. Machine Learning and the Physical Sciences workshop @ NeurIPS 2022. paper

• Shah K., Stiller P., Hoffmann N., Cangi A. (2022) Physics-Informed Neural Networks as Solvers for the Time-Dependent Schrödinger Equation. Machine Learning and the Physical Sciences @ NeurIPS 2022. paper

• Stiller, P., Bethke, F., Böhme, M., Pausch, R., Torge, S., Debus, A., Hoffmann, N. (2020). Large-scale Neural Solvers for Partial Differential Equations. SMC 2020: Driving Scientific and Engineering Discoveries Through the Convergence of HPC, Big Data and AI, CCIS. 1315, 20-34. paper