Goal: Predict a hidden physical parameter from noisy, incomplete measurements of a moving system's trajectory.
Every trajectory in this competition comes from the same kind of nonlinear dynamical system, but each one is shaped by a hidden parameter you can't see directly — only its effect on the motion. Your job is to recover that parameter from imperfect data: measurements with noise, occasional gaps, and uneven timing, much like a real sensor would produce.
There's no single obvious feature that hands you the answer. The system is nonlinear, so the hidden parameter changes the shape of the motion, not just its size — which means careful exploratory analysis, good feature engineering, and thoughtful modeling all have real room to pay off. Whether you approach this with classical statistics, tree-based models, sequence models, or a bit of applied math, there's a path to a strong score, and more than one way to find it.
The Physical Setup The trajectories are generated by a two-dimensional nonlinear dynam system describing a small mass on a spring-like system. It features self-sustaining, amplitude-dependent damping and a stiffening restoring force. A single number controls how strongly the system's tendency to settle into a rhythm asserts itself; this number is your hidden target.
Data Characteristics
You receive simulated imperfect measurements of the trajectory:
- Measurement noise: Every recorded x and y value has independent Gaussian noise added.
- Missing observations: Roughly 7% of readings are missing (NaN), occurring as isolated drops or short gaps.
- Irregular sampling: The time between consecutive measurements jitters around a nominal spacing.
Strategies Worth Trying - Statistical summaries: Spread, range, energy, and autocorrelation at a few lags. - Spectral features: Computed carefully given irregular sampling (e.g., Lomb-Scargle periodogram). - Tree-based models: Random Forest or gradient boosting on engineered features. - Sequence models: Consuming raw trajectory data directly to capture waveform shape information. - Applied math: Directly fitting the governing equation to candidate trajectories.
Evaluation Submissions are scored using Mean Absolute Error (MAE) between predicted and true parameter values. Lower scores are better. Root Mean Squared Error (RMSE) is also reported as a secondary diagnostic.