Physics-informed Neural Networks and Machine Learning II

Machine learning (ML) is a powerful tool for data analysis, yet integrating physical symmetries and laws into the learning process remains an important goal for learning new physics with ML. A common way of integrating physics into ML is to add a regularization term describing a known physical constraint into the training loss, as used in physics-informed neural networks (PINNs). Rather, here we demonstrate a novel way to incorporate physics in ML by using neural networks (NNs) as universal approximators to nonlinear force laws and validating the model's predictions solely with experimental data. We use a dynamic, many-body system of microparticles called dusty plasma. Inside a plasma, dust particles (~10 microns) experience complex forces such as non-reciprocal, plasma-mediated pairwise interactions, environmental electrostatic forces, and drag forces. We build a model using Newton’s 2nd law, specifying different symmetries in the inputs to NNs representing these forces, and fit the sum of these forces to the particles' experimental acceleration with remarkable cross-validation R2 of 0.99.Note that correctly fiting the sum of these forces does not necessarily indicate that the fitting of each force component is correct, which is extremely challenging to verify since the ground truth of each force component is unknown in the experiments. To overcome this challenge, we interpret the NNs prediction in terms of physical parameters like charge and electric field and use physical laws (e.g. Maxwell’s equations) to validate these predictions. Our ability to identify new physics from experimental data demonstrates how ML-powered approaches can guide new routes of scientific discovery in many-body systems. Furthermore, we anticipate our ML approach to be a starting point for inferring laws from dynamics in a wide range of many-body systems, from colloids to living organisms.