Simultaneous inference of environmental and interaction forces in collective dynamics

What the math gives to ML

The paper provides a constructive decomposition of multi-agent dynamics into an agent-wise environmental force and a permutation-symmetric pairwise interaction force, learned simultaneously from trajectory derivatives. Its transferable asset is not the least-squares solver itself, but the structural separation: each agent's local state and velocity contribution is modeled independently from a shared distance-based message-passing kernel, making the learned dynamics more interpretable and potentially more data-efficient than an unconstrained graph neural ODE. A practical neural adaptation is to impose this additive factorization on an equivariant world model and train it with acceleration matching, while using ablations and residual gates to determine whether the environmental or interaction branch is actually needed.