Research map / Probabilistic and scientific modeling / Dynamical systems
Deconstructing the Inductive Biases of Hamiltonian Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add second-order structure (dq/dt = v, learn acceleration) to a NODE | NODE on OpenAI Gym MuJoCo transition models · MuJoCo HalfCheetah, Hopper, Swimmer | rollout error (test) | Helped |
| Use a Hamiltonian (HNN) bias instead of plain NODE | transition models on MuJoCo · MuJoCo HalfCheetah, Hopper, Swimmer | rollout error | Hurt |
| Add second-order structure to NODE on damped pendulum systems | NODE · n-body pendulums with drag | rollout error | Helped |
| Add symplectic regularizer (symplectic error penalty) to NODE (ablation) | NODE on chain and spring pendulums · Chain 1-3, Spring 1-3 | test rollout error | No clear effect |
| Impose second-order structure on NODE (ablation) | NODE and HNN on chain/spring pendulums · Chain 2-4, Spring 2-4 | rollout error | Helped |
| Enforce energy conservation of learned Hamiltonian (HNN) vs unconstrained NODE | HNN vs NODE · chain and spring pendulums | energy violation conditioned on rollout error | No clear effect |
| Switch training loss from l2 to l1 (ablation) | NODE, NODE+SO, HNN · Chain and Spring pendulums | rollout error | No clear effect |
| Use Cartesian-like simpler functional form (spring pendulum) so Hamiltonian and vector field complexity comparable | HNN vs NODE+SO · spring pendulums vs chain pendulums | rollout error | Mixed |
| Add second-order structure to NODE on Gyroscope, Magnet, Rotor systems | NODE · Finzi et al. 2020 additional systems | rollout error | Mixed |
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