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Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add explicit constraints to the model (ablation) | physics-informed GNNs · n-pendulum | rollout and energy error | Helped |
| decouple kinetic and potential energies (Hamiltonian GN to Hamiltonian GNN) (ablation) | HGN · spring and pendulum systems | rollout and energy error | Helped |
| decouple kinetic and potential energies (Lagrangian GN to Lagrangian GNN) (ablation) | LGN · spring systems | momentum error | Helped |
| use physics-informed bias instead of purely data-driven GNN (ablation) | FGNN · spring and pendulum systems | rollout and energy error | Helped |
| use physics-informed bias instead of purely data-driven GNN (ablation) | FGNN · 3D elastic solid | rollout and momentum error | No clear effect |
| use graph-based versions instead of fully connected MLP counterparts (ablation) | LNN and HNN · 3-pendulum | rollout and energy error | Helped |
| use Hamiltonian GNN formulation versus Lagrangian GNN | HGNN · spring systems | rollout and energy error | Helped |
| use Hamiltonian GN (HGN) on pendulum versus spring systems (ablation) | HGN · pendulum systems | rollout and energy error | Hurt |
| train on small system and test on 10x larger unseen system sizes | graph-based physics-informed GNNs · 5/10/20-pendulum and 5/20/50-spring | rollout and energy error | No clear effect |
| add noise to training data | physics-informed GNNs · appendix noise study | error: 10-fold increase in error | Hurt |
| Lagrangian GN family with double derivative | LGN family · training and inference time | time | Hurt |
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