# (4) Machine learning in many-particle systems

**[PIs: ****Griebel****, ****Grimme****, ****Neese**** ] **

Over the last years, the amount of experimental and simulation data has resulted in the emergence of the so-called data-driven science. Machine learning (ML) models have the potential to learn and describe efficiently very complex nonlinear mappings between input and output data. Thus, ML and data analysis techniques are promising tools to derive accurate and cost efficient potential models for many-body systems and also energy functionals for DFT approaches. The ability for algorithms to “learn” and “adapt” offers the possibility for efficient, fast, and unbiased improvement in decision making. Here, one often follows a so-called grey-box ansatz, which unifies in some sense all paradigms. The aim of so-called white-box-models is an exact physical description of the modeled system, while the purpose of the so-called black- box-models is to reproduce the input-output behavior of a system (by e.g. deep learning neuronal networks). To establish a white-box-model is in many cases too complex and the amount and quality of data for a black-box-model is often insufficient. Hence, approaches which are based on the mixture of black and white models, i.e. grey-box-models, are in general a promising and powerful tool. Here, we attempt to describe the emergent behavior of many-particle systems using ML algorithms. Since ML techniques provide the possibility to describe high-dimensional and highly nonlinear mappings, they are a promising tool to derive novel data-driven efficient models for many-particle systems, e.g. ML based models for energy-functionals and/or interaction potentials. In particular, in the case of general highly non-linear energy functionals, one has in principle to deal with infinite dimensional spaces. Here, the combination of extrapolative low dimensional physical models with ML techniques is surely a very promising approach.