The talk needed to be canceled and will be rescheduled.
Date: April 17, 2024, 12:00–13:30
Speaker: Prof. Dr. Uwe Naumann (RWTH Aachen University)
Location:
Weyertal 86–90, 50931 Cologne
Mathematical Institute (Google Maps, OpenStreetMap)
Seminar Room 1 (Room 0.05)
Title: Derivatives and Applications for Learning Derivatives
Abstract: Surrogates for numerical simulations can be learned (by "machines") through sampling inputs to the simulation to obtain desired outputs. Adequate matching of the latter is likely to not be sufficient for the numerical methods (e.g. calibration or optimal control) to be applied to the simulations and hence to their surrogates. Consistency of simulation and surrogate up to a certain order of differentiation may be required. The "machine" needs to learn values as well as first and possibly higher derivatives. Algorithmic differentiation [1] helps to generate this data.
We discuss two rather different recent applications of differential machine learning (also known as Sobolev training). [2] addresses pruning of oversized artificial neural networks based on interval adjoint significance analysis. A new exact matrix-free Newton method is presented in [3]. Its extension to surrogates of appropriate structure is the subject of ongoing research.
[1] Naumann: The Art of Differentiating Computer Programs. SIAM 2012.
[2] Kichler, Afghan, Naumann: Towards Sobolev Pruning. Under review for PASC'24. See also arXiv:2312.03510.
[3] Naumann: A Matrix-Free Exact Newton Method. To appear in SISC, SIAM. See also arXiv:2305.01669.