Infer force laws in many-body dusty plasma systems

Scientific laws describing natural systems may be more complex than our intuition suggests, and thus how we discover laws must change. Machine learning (ML) models handle large quantities of data, but their structure should match the underlying physical constraints to provide useful insight. Here we demonstrate a ML model where the physics can be built in, step by step, to infer forces and learn new laws from experimental data in dusty plasmas. Trained solely on the 3D experimental particle trajectories, our model accounts for the inherent symmetries and varying number of non-identical particles, and learns the effective non-reciprocal force law governing their motion, and extracts the mass and charge of each particle. The model validates itself by predicting the masses of each particle in two independent ways with excellent agreement. Furthermore, we discovered a new scaling law in our system that a particle's charge is proportional to its mass to the power of 0.74, different from 1/3 predicted by OML theory. This implies that two particles of different sizes at the same position in the plasma sheath have a different floating potential. Outside of dusty plasmas, these results guide new routes of discovery using physics-tailored ML in many-body systems.