Parametric model reduction of mean-field and stochastic systems via higher-order action matching

We learn models of population dynamics of physical systems that feature stochastic and meanfield effects and that depend on physics parameters. Building on the Benamou-Brenier formula and action matching [2], we infer population dynamics from a simulation-free variational objective. The inferred gradient fields can then be used to predict the populations dynamics for unseen physics parameters. Higher-order quadrature is critical for accurately estimating the training objective. HOAM yields orders of magnitude speed-up compared to classical numerical models.