A minimalistic approach to physics-informed machine learning using neighbour lists as physics-optimized convolutions for inverse problems involving particle systems

This study proposes a hybrid approach for combining mechanistic (first principle) and Machine Learning models. This approach applies to discrete (particle-based) systems and continuous systems that can be recast as a particle problem by a framework like Smoothed Particle Hydrodynamics. The governing equations are written as a set of equations describing the motion of the particle system. Artificial Neural Networks are used to derive from data the forces acting on the particles, while the system's path in the state-space is calculated with the equation of motion. This ensures that fundamental physical principles such as Newton's laws of motion are always satisfied in a strong sense. Neighbour lists automatically introduce dimensionality reduction into the system by functioning as physics-optimized convolutions. Therefore, the network can be smaller, simpler, and more easily trainable than other physics-informed machine learning models. The proposed technique is applied to three inverse modelling problems. The method is designed to learn the pairwise forces acting between particles without knowing these forces from the training data. In fact, the training data contains the total force acting on each particle, not the pairwise forces between pairs of particles. Data for Molecular Dynamics, Smoothed Particle Hydrodynamics and Discrete Element Method simulations are fed into the model that ‘extracts’ their physics and reproduces the simulations with a high degree of accuracy. The model's capability for generalization is noteworthy. As long as the underlying physics remains the same, the model can predict the dynamics of systems with geometries and boundary conditions very different from those of the training dataset. As a remarkable example, a model trained surface-flow data also correctly replicates channel flow.