Multi-Level Neural Networks for PDEs with Uncertain Parameters

Multi-Level Neural Networks for PDEs with Uncertain Parameters

This seminar will be delivered by Benjamin Sanderse where he will be discussing a multi method for partial differential equations with uncertain parameters.

The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good approximation independent of the actual grid level. This method uses this structure by employing a sequence of convolutional neural networks, that are well-suited to automatically detect local error features as latent quantities of the solution. Furthermore, by using the concept of transfer learning, the information of coarse grid levels is reused on fine grid levels in order to minimize the required number of samples on fine levels. The method outperforms state-of-the-art multi-level methods, especially in the case when complex PDEs (such as single-phase and free-surface flow problems) are concerned, or when high accuracy is required.

If you would like to attend this talk, please get in touch with Wouter Edeling from the SC group at CWI.

Please visit the seminar for Machine Learning and UQ in Scientific Computing webpage to get more information on upcoming seminars.