Structure-preserving deep neural networks to accelerate the solution of the Boltzmann equation

• Applicant: Professor Dr. Martin Frank
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 464075789

The goal of this project is to use deep neural networks as building blocks in a numerical method to solve the Boltzmann equation. This is a particularly challenging problem since the equation is a high-dimensional integro-differential equation, which at the same time possesses an intricate structure that a numerical method needs to preserve. Thus, artificial neural networks might be beneficial, but cannot be used out-of-the-box. Furthermore, using them in a numerical solver requires new numerical analysis techniques. The project therefore touches upon the applications point of view of deep learning with a focus on interpretability and robustness, and on the mathematical methodologies point of view to solve partial differential equations.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2298: Theoretical Foundations of Deep Learning
• Co-Investigator: Dr. Tianbai Xiao