Dusty plasma is a mixture of ions, electrons, and macroscopic charged particles that is commonly found in space and planetary environments. The particles interact through Coulomb forces mediated by the surrounding plasma, and as a result, the effective forces between particles can be non-conservative and non-reciprocal. Machine learning (ML) models are a promising route to learn these complex forces, yet their structure should match the underlying physical constraints to provide useful insight. Here we demonstrate and experimentally validate an ML approach that incorporates physical intuition to infer force laws in a laboratory dusty plasma. Trained on 3D particle trajectories, the model accounts for inherent symmetries, non-identical particles, and learns the effective non-reciprocal forces between particles with exquisite accuracy (R^2>0.99). We validate the model by inferring particle masses in two independent yet consistent ways. The model's accuracy enables precise measurements of particle charge and screening length, discovering large deviations from common theoretical assumptions. 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.