This Emerging Field aims to develop novel methods, through combining machine learning and mathematical process simulation, which are able to derive effective dynamical laws from data. As a result, we anticipate to obtain models which generate understanding and physical insights, and can be simulated efficiently, resulting in unprecedented speed-ups compared to the often intractable classical direct simulation methods such as for the time-dependent Schrödinger equation in quantum processes.
This program faces several challenges. First, current machine learning methods are often black-box approaches, which are not sufficient for scientific simulation and measurement data. And, second, current machine learning methods study mostly static, stationary, and complete data, however scientific data is often dynamic, nonstationary, incomplete, multimodal, and multiscale.
Consequently, the projects within this Emerging Field focus either on the development of a theory for machine learning, in particular, deep learning, or approach this problem complex from the application side. Moreover, the projects are typically characterized by a high degree of interdisciplinarity as well as by utilizing a combination of numerous mathematical areas.
Scientists in Charge: Jens Eisert, Gitta Kutyniok, Klaus-Robert Müller