Discovering Interactions Laws of Multiparticle Systems with Lagrangian Neural Networks

Physical laws in nature, such as gravitational, electromagnetic, ionic and covalent interactions govern the spatial and temporal evolution interacting systems. Realistic modeling of these systems require accurate prediction of these interactions. Traditionally, this is achieved based on empirical relationships or developing models that are fitted against first principle simulation results. Here, we present momentum conserving Lagrangian neural network (MCLNN), using which any interaction law that governs the dynamics of multiparticle systems can be directly learnt. The interaction laws are learnt from the trajectory with on information on the functional form of the interactions themselves. We also show that the system is scalable to any size once trained. To demonstrate the wide applicability of MCLNN, we take several examples including atomic, mesoscale, continuum, and experimental systems. For all the examples, we demonstrate that MCLNN can accurately predict the interaction law, thereby revealing the hidden interaction in nature.