Physics-Inspired Machine Learning for Long-Range Interactions

• Applicant: Dr. Marcel Langer
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation ; Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing ; Computer-Aided Design of Materials and Simulation of Materials Behaviour from Atomic to Microscopic Scale
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 544947822

Computer simulations of molecules and materials are an indispensable tool for physics, chemistry, and materials science. Many simulation methods are available, with different tradeoffs between computation cost and accuracy. The most accurate and computationally expensive ones are first-principles methods, which approximately solve the electronic Schrödinger equation, obtaining high accuracy at high computational cost. On the other end are force fields, simple analytical approximations that are fast to evaluate, but require careful parametrisation and an explicit model of desired physical interactions. Machine learning (ML) is increasingly used to bridge the gap between these two extremes, aiming to simultaneously achieve high accuracy and low computational cost. ML force fields (MLFFs) are obtained via highly flexible regression models that are trained on first-principles reference calculations and then used as surrogate models during molecular dynamics simulations. However, most MLFFs are based on a locality assumption: The total potential energy is partitioned into atomic contributions, which are computed based on the local environment of each atom. This enables linear scaling of computational cost as well as the ability to generalise to systems of different size, but disregards all long-range interactions. To accurately model systems such as molecular crystals, ionic liquids, or metal-organic frameworks, which feature dispersion, electrostatics, and other non-local interactions, more general MLFFs are required. At present, only partial solutions are available for this, including models for specific long-range interactions: Traditional force fields include pairwise long-range energy contributions that can be evaluated efficiently, but require advance knowledge of expected interactions and have limited flexibility. Current message-passing neural networks, which build up longer-range interactions through repeated interactions between atomic neighbourhoods, can be used to efficiently learn many-body interactions, but cannot express truly long-range behaviour. All-to-all models such as transformers can in principle learn all interactions, but are difficult to scale and generalise. To overcome these limitations, we propose to develop a neural network architecture that uses physical interactions as an equivariant long-range message passing mechanism. This will enable the data-driven modelling of interactions ranging from simple pairwise terms to complex many-body interactions in a unified framework. Being based on physical principles, the model will be interpretable, can be evaluated efficiently with available computational methods, and respects physical asymptotic behaviour. This development will enable the accurate modelling of systems that are challenging for current MLFFs, such as molecular crystals, ionic liquids, and metal-organic frameworks, at system sizes and time scales that are inaccessible to first-principles methods.

• DFG Programme: WBP Fellowship
• International Connection: Switzerland
• Host: Professor Dr. Michele Ceriotti