Gitta Kutyniok, Frank Noé, Barbara Zwicknagl
Alex Goeßmann (TU)
01.01.2019 – 31.12.2021
This project will develop a profound theoretical understanding of neural networks for extracting dynamical laws from complex data, focusing predominantly on expressivity aspects. We aim to derive various optimality results for the design of the architecture and to analyze the sample complexity of this problem.
During the first year of the funding period, we have studied the case of linear activation functions and provided a tensor network regression ansatz for learning non-linear dynamical laws. Furthermore, similarities between the field of function identification and dynamical law extraction have been analyzed. In current projects, we bound the sample complexity of identifying functions from data, where we apply concepts from compressed sensing and the chaining theory of stochastic processes.
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