Checklist USA-NA-AIO 2026 Round 2 · Task 2
Recovering a Single Source Central Field from Vector Field Observations
From a 64×64 grid of force vectors, predict the location of a single source and the field magnitude at 100 radii.
The task
Problem 2 (70 points, open-ended) considers a central force field on [−1, 1]^2 generated by one unknown source; the magnitude function f_s(r) is unknown and may differ between samples. Each sample is a (64, 64, 2) tensor of vector measurements.
Training (10,000 samples) and validation (2,000 samples) sets include the source location and f_s at predefined radial checkpoints; the test set has 3,000 samples. For each test sample the contestant predicts (x_s, y_s) and f_s(r_i) for r_i = 0.02 + 0.02i, i = 0…99 (102 values). The baseline is a CNN that outputs the 102 numbers directly.
Abridged by SOTA from the official materials. The official statement has the exact rules, and it wins wherever this summary differs.
At a glance
- You get
train.npz,val.npz,test_inputs.npz,r_grid.npyand a sample submission.- You submit
- A prediction CSV, a notebook and a .docx report, each named Central_Field_LastName_FirstName_SchoolName.
- Scoring
- Per-sample error = 10^3 × (|Δx| + |Δy|) + 3 × 10^−3 × RMSE over the 100 magnitudes; score = mean over test samples (lower is better). Missing location → location error 10; missing magnitude → field error 10^7/3. Final score = (X_baseline − X)/(X_baseline − X_best) × 100%, where X_best = min(jury expert model, best contestant); 0 if worse than the baseline.
- Format
- 2026 USA-NA-AIO Round 2, Day 1 (4 April 2026).