Cosmin Anitescu: Methods Based on Artificial Neural Networks for the Solution of Partial Differential Equations

Machine Learning Seminar presentation

Topic: Methods Based on Artificial Neural Networks for the Solution of Partial Differential Equations

Speaker: Dr. Cosmin Anitescu, Bauhaus-Universität Weimar

Time: Wednesday 2020.10.28, 10:00 CET

How to join: Please contact Jakub Lengiewicz

Abstract:

Machine learning and methods based on artificial neural networks have become increasingly common in a variety of topics for areas such as image processing, voice recognition, and object detection. The success in these areas has also led to optimized hardware and software solutions for efficiently training large neural networks and solving previously intractable problems. There is also a great deal of interest in using these techniques for solving complex engineering problems.

In this talk, I will give a brief overview of some algorithms for solving partial differential equations using artificial neural networks, particularly with regard to dealing with the boundary conditions. I will also discuss some possibilities for adaptively choosing the training points and possibilities for further improvements in the efficiency and reliability of neural network-based PDE solvers.

Additional material:

(1) An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications https://doi.org/10.1016/j.cma.2019.112790 or https://arxiv.org/abs/1908.10407