  Scientific laws describing natural systems may be more complex than our
intuition can handle, and thus how we discover laws must change. Machine
learning (ML) models can analyze large quantities of data, but their structure
should match the underlying physical constraints to provide useful insight.
Here we demonstrate a ML approach that incorporates such physical intuition to
infer force laws in dusty plasma experiments. Trained on 3D particle
trajectories, the model accounts for inherent symmetries and non-identical
particles, accurately learns the effective non-reciprocal forces between
particles, and extracts each particle's mass and charge. The model's accuracy
(R^2 > 0.99) points to new physics in dusty plasma beyond the resolution of
current theories and demonstrates how ML-powered approaches can guide new
routes of scientific discovery in many-body systems.
