Amortized Neural-Symbolic Inverse Dynamics: Robust and Invariant Parameter Inference via Latent Dynamics

We propose an amortized neural-symbolic framework for physical parameter inference in dynamical systems. Building on the CAMEL meta-learning framework, whose latent task embeddings carry provable identifiability guarantees, we train a post-hoc MLP to directly recover physical parameters that are nonlinearly related to trajectory data, without per-trajectory optimization or explicit knowledge of the dynamics. We distill this neural mapping into closed-form symbolic expressions via symbolic regression, achieving robust out-of-distribution generalization that validates the recovered physics. To handle realistic conditions, we address measurement noise through domain randomization and improve robustness to unobserved nuisance variables via a structured grouped training strategy. Experiments on a simulated 2-DOF robotic arm show competitive accuracy with classical identification baselines at $\sim1000\times$ faster inference, with interpretable parameter mappings and superior noise robustness.