An arXiv preprint reports that its PhyODE model recorded lower trajectory errors than the strongest listed baseline when forecasting from held-out initial states. In the long-horizon OOD-Initial setting—30 observed steps followed by 60 predicted steps—its average displacement error was reported as 33.1% lower and its final displacement error as 31.0% lower.
Average displacement error, or ADE, summarizes prediction error across all future steps. Final displacement error, or FDE, measures the error at the last future step. The benchmark also tests shorter Short and Mid forecast windows.
A benchmark designed to test more than motion
ExPhy contains 24,000 simulated dynamic scenes, each with three to eight objects. ExPhy-A contains 20,000 scenes, split into 16,000 for training and 2,000 each for validation and testing. ExPhy-B and ExPhy-C each contain 2,000 held-out test scenes.
ExPhy-A is the in-distribution split. ExPhy-B tests shifts in physical parameters, while ExPhy-C tests shifts in initial states. The benchmark gives each object simulator-derived labels for mass, friction and restitution, the property linked to how collisions rebound.
PhyODE estimates those properties explicitly, then combines frictional dissipation and collision updates with a residual Neural ODE—a learned correction to the physical calculation—using the RK4 integration scheme. Models were trained on ExPhy-A, selected with validation-based checkpoints and evaluated on ExPhy-B and ExPhy-C without fine-tuning.
Longer forecasts favored the structured model
On the Long horizon, PhyODE's reported ADE/FDE on the in-distribution ExPhy-A split were 0.36/0.75. On ExPhy-C, it recorded 0.97/2.00, compared with the second-best reported result of 1.45/2.90, and it had the best ADE on ExPhy-B.
The paper also reports the best results for PhyODE in zero-shot transfer to ComPhy trajectories: ADE/FDE of 0.12/0.20 at Short, 0.37/0.65 at Mid and 0.51/0.82 at Long.
Motion accuracy did not guarantee property accuracy
The physical-property estimates showed a tougher result under the shifted-parameter test. Average normalized mean absolute error was 0.15 on ExPhy-A and 0.42 on ExPhy-B for the strongest reported models, with errors increasing especially for mass.
An ablation of PhyODE's supervision targets made the gap clearer. Property-only supervision produced NMAE values of 0.15 on ExPhy-A and 0.42 on ExPhy-B. Trajectory-only supervision produced 0.40 and 0.68, while joint supervision produced 0.21 and 0.50. Joint training therefore remained less accurate for property estimation than direct property supervision.
The authors conclude that low trajectory error does not necessarily mean a model has accurately recovered mass, friction or restitution. Forecasting motion and identifying the physical properties behind it are separate tests.
The evidence remains inside simulation
In a component ablation, full PhyODE recorded ADE/FDE of 0.97/2.00 on ExPhy-C. The version without explicit physics reported 1.80/3.41, while the version without the Neural ODE reported 1.12/2.30; the reported degradation also appeared on ExPhy-A and ExPhy-B.
The evidence is limited to simulated scenes and the stated evaluation protocol, including controlled shifts in physical parameters or initial states. The paper does not report validation on real-world physical scenes, p-values, confidence intervals, uncertainty estimates or robustness across training seeds, so the results do not establish generalization beyond the listed simulator and settings.
The paper is an arXiv version 1 preprint dated 20 Aug 2026. It states that the ExPhy code and data are available through the project's GitHub repository.
Paper data and sources
Original title: ExPhy: A Benchmark for Explicit Physical Property Learning in Multi-Object Trajectory Forecasting
Authors: Rui Wang, Yeteng Wu, Xianlin Zhang, Mengshi Qi
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text