Deep learning observables of solutions of nonlinear hyperbolic partial differential equations

The goal of the project is to make headway in the analysis of DNNs in the application to numerical methods for nonlinear hyperbolic partial differential equations (PDEs).

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Deep neural networks (DNNs) have been enormously successful in tasks varying from image recognition to optimal control of mechanical components. However, their reason for success is poorly understood, and it is at present very difficult to analyze or predict the emergent properties of a given DNN.

The goal of the project is to make headway in the analysis of DNNs in the application to numerical methods for nonlinear hyperbolic partial differential equations (PDEs). We will establish a framework for the analysis of such numerical methods, with the aim of determining whether a DNN numerical method is stable, accurate and convergent.

Ultimately, this work will contribute to the knowledge about the robustness and predictability of machine learning algorithms when applied to real-world problems.

Requirements

  • MSc in mathematics, with an emphasis on PDEs.
  • Candidates with knowledge and experience with numerical methods for PDEs, particularly hyperbolic PDEs, as well as machine learning, will be prioritized.

Supervisors

Associate Professor Ulrik Skre Fjordholm

Call 2: Project start autumn 2022

This project is in call 2, starting autumn 2022. 

Published Aug. 17, 2020 4:48 PM - Last modified Nov. 17, 2020 3:23 PM