Physical Dynamics and Constraints › Limitations and Impact

Physics priors are only as good as the physics assumed. An autonomous unforced conservative architecture preserves its learned invariant under exact continuous flow even when that makes it a poor model of driven or dissipative data. A rigid-body backbone with the wrong friction model can mispredict a lubricated joint or slipping tire. An additive residual may correct some backbone mismatch, but limited capacity or structural constraints may prevent the repair, while a flexible residual can hide a missing mechanism. Treat each prior as a falsifiable claim. Residual tests that find no detectable bias, autocorrelation, state dependence, or miscalibration are evidence, not proof, that the backbone is adequate.

Hard contact remains a major challenge because complementarity and event timing can make gradients discontinuous or inaccurate. Learned contact models can also face sparse coverage of short impact events and new contact geometries. Event-aware differentiation, compliant approximations, interactive data collection, and simulator-based training address different parts of the problem; none removes the need to evaluate contact-rich rollouts directly. We will revisit structured simulators and differentiable physics in Part IV, Chapter 4.

There is also a subtler tension between interpretable physical state and flexible learned representation. Direct constraints want positions, velocities, and contact geometry; latent models may discover coordinates with no immediate physical meaning. One active direction builds physics into a relational skeleton of objects, contacts, and interactions while leaving perceptual details learned. This connects to compositionality and systematic generalization in Part IV, Chapter 6, but its value remains an empirical design choice rather than a universal prescription.

Physics-structured learning has produced methods that enforce selected invariants, fit physical parameters through differentiable simulators, and improve some long-horizon benchmarks when the assumed structure matches the system. Hamiltonian and Lagrangian networks learn scalar functions from data while enforcing a designer-chosen variational form; they do not discover arbitrary symmetries automatically. These constraints do not calibrate uncertainty under shift, and a misspecified prior can create confident systematic error. For a downstream planner, the useful guarantee is therefore only the property enforced and independently tested. A correct, applicable conservation law can be an unusually strong inductive bias, but it does not replace data fit, uncertainty estimation, or model-mismatch checks.