Neural functional theory for inhomogeneous soft matter

• Applicant: Professor Dr. Matthias Schmidt
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 551294732

Soft matter forms a broad class of materials and systems that are relevant for everyday and industrial products, while simultaneously providing well-controlled and well-characterized model systems that give detailed opportunities for studying fundamental physical effects of self-organization and collective structure formation. Although mechanically soft, typical liquid and gel systems are both dense and strongly correlated on microscopic scales. These features render the development of a quantitative understanding based on first principles a challenging undertaking. In the project we aim to develop, to test and to apply a rigorously based statistical mechanical framework for describing the behaviour of a wide range of soft matter systems from dense liquids to gel states. Machine learning is used to make practical progress in the fundamental description of the physics that emerges from the correlated interactions of the constituent particles at microscopic scales. In particular the use of functional relationships, which are established in a formally exact way via classical density functional theory, forms the basis for the construction of neural networks that act as concrete models to represent the many-body physics in a computationally efficient and conceptually flexible way. Both automatic differentiation and efficient numerical functional integration shall be used to test and to investigate mathematical relationships between these neural functionals. Specifically, the project is aimed at establishing a systematic, first-principles based, machine-learning-supported understanding of correlation effects in i) dense liquids beyond the hard sphere packing paradigm, of ii) liquids with complex multi-body interparticle interaction potentials, such as water, and of iii) the fundamental differences of correlations in liquids and in gels, where the target is a specific gel formation process that applies in equilibrium. The proposed research aims at bridging the gap from the first-principles study of idealized model systems to realistic Hamiltonians for complex materials. Strong correlation and adsorption behavior in spatially inhomogeneous systems shall be investigated.

• DFG Programme: Research Grants