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+# Reproduction: BALLAST (ICML 2026)
+
+Independent, from-scratch reproduction of
+
+> **BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter
+> Trajectories under Spatio-Temporal Vector Fields**
+> Rui-Yang Zhang, Henry Moss, Lachlan Astfalck, Edward Cripps, David Leslie
+> ICML 2026 · OpenReview `0xOj6kVMbb` · arXiv [2509.26005](https://arxiv.org/abs/2509.26005)
+
+There is **no official code release** for this paper. Everything here was written
+from the paper text (main text + appendices A–H).
+
+## Layout
+
+```
+ballast/
+  kernels.py      Helmholtz + Matern-3/2 kernels, analytic derivatives,
+                  extended GP f = [f, d_t f]^T  (paper Sec. 2.2, 4.1, B.2)
+  spde.py         SPDE / state-space formulation, exact propagation (Sec. 4.1, App. F)
+  gp.py           regression, posterior sampling, information-gain utilities,
+                  rank-q Gram determinant updates (App. B.1, C.1, E.2)
+  trajectory.py   Lagrangian advection + observation model (Sec. H.1)
+  policies.py     UNIF, SOBOL, DIST-SEP, EIG, BALLAST-true, BALLAST-opt (Sec. H.3)
+  experiment.py   active-learning campaign driver, iso-performance (Sec. 5.2)
+tests/            correctness checks (see below)
+run_job.py        entry point: bench | synth | suntans | ablation | spde_cost
+hf_entry.py       Hugging Face Jobs wrapper
+analyze.py        raw JSON -> per-claim numbers
+plot.py           Plotly figures + raw CSV
+fit_suntans.py    put the SUNTANS field in the paper's units; fit the surrogate
+data/
+  extract_suntans.py   derive surface u,v from the SUNTANS harmonic atlas
+```
+
+## Running
+
+```bash
+uv venv && uv pip install jax numpy scipy matplotlib plotly pandas pytest
+.venv/bin/python -m pytest tests/ -q            # 13 correctness tests
+.venv/bin/python run_job.py bench               # one full-scale campaign per policy
+```
+
+On a GPU via HF Jobs:
+
+```bash
+hf jobs uv run --flavor a100-large --timeout 2h -d \
+  -e BALLAST_ARGS="synth --seed-lo 0 --seed-hi 10 --out /tmp/o.json --bucket txus/ballast-repro-results" \
+  -s HF_TOKEN=$HF_TOKEN hf_entry.py
+```
+
+## Tests
+
+`tests/` encodes what must be true for the reproduction to mean anything:
+
+- `test_spde.py::test_posterior_sampling_is_exact_with_nongridded_observations` —
+  the Sec. 4.1 sampler is **exact**, compared analytically (not by Monte Carlo)
+  against a dense GP, with observations at non-gridded Lagrangian locations.
+- `test_spde.py::test_prior_matches_dense_gp` — SPDE prior ≡ `k_tHelm` exactly.
+- `test_kernels.py::test_matern32_second_derivative_at_zero` — the Sec. H.2
+  clipped-distance autodiff trap (`d^2_{tt'}k = 3` at `t=t'`, not 0).
+- `test_padding.py` — the shape-padding used for performance is provably inert.
+
+## Deviations from the paper, and why
+
+1. **Observations are conditioned at the cell centre, not the drifter's exact
+   position.** The ground-truth field exists only on the grid and a drifter
+   measures "the velocity of the grid cell containing the location" (Sec. H.1),
+   so the measurement *is* a noisy observation of `f` at the cell centre.
+   Regressing it at the exact position is misspecified: for the Sec. 5.2 setup
+   the within-cell field variation has sd ≈ 0.29, about 3× the assumed
+   `sigma_obs = 0.1`. A GP told the noise is 0.1 then interpolates
+   discretisation error — the posterior mean overshoots to ~3× the true field
+   range and the field error *rises above the prior* as drifters are added.
+   Snapping removes the misspecification exactly.
+
+2. **Utility uses `logdet(I + sigma^-2 K)`, per App. C.1, not the main text's
+   `logdet(I + sigma^2 K)`.** The main-text form is a sign-of-exponent typo;
+   with `sigma = 0.1` the two differ by 1e4 inside the logdet and rank
+   candidates differently.
+
+3. **SUNTANS region and units are inferred** (Sec. 5.3 states neither). See
+   `fit_suntans.py` for the reasoning and the agreement it produces.
+
+4. The paper's stated SUNTANS "true" stream-kernel values (`psi_ls=4`,
+   `psi_var=0.01`) lie **outside its own stated BALLAST-opt bounds**
+   (`[0.1,1]` and `[0.1,5]`, Sec. H.3). We use the stated values for
+   BALLAST-true and the stated bounds for BALLAST-opt.
+
+## Artifacts
+
+- Code + data: <https://huggingface.co/datasets/txus/ballast-repro>
+- Raw results: <https://huggingface.co/datasets/txus/ballast-repro-results>
+
+SUNTANS ground truth derives from the **Northern Australia Internal Tide
+Climatology** (Rayson et al. 2021, CC BY, DOI
+[10.26182/8jx9-m532](https://doi.org/10.26182/8jx9-m532)), read with the physics
+of [`mrayson/iwatlas`](https://github.com/mrayson/iwatlas).