tidal_friction_inverse

Sparse-Gauge Tidal Friction Field Inversion

Invert seabed friction from sparse tide gauges

tidal_friction_inverse Earth & Energy Geoscience

instruction.mdthis is what the agent is given

Design a calibration method for the spatially varying seabed friction field of a tidal basin, starting from a deliberately weak homogeneous-friction solver. Minimize complex tidal-elevation RMSE at unobserved gauges; your submitted method is re-run on sealed basins and sealed gauges for scoring.

Hard Constraints

Modify only /app/methods/main/solver.py as the final submission.
Keep the public function estimate_logf(case) and return one finite numpy array with shape (24, 24).
Use only information in case; do not read validation heads inside the solver.
The returned log-friction field must stay in [-3.0, 1.0].
A solver call must finish within 60 seconds on two CPU cores and use no network.

What You Have

/app/problem.py: the frequency-domain shallow-water tidal simulator (solve_field / simulate) and case schema.
/app/data/visible_cases.npz: six calibration cases, each with known bathymetry, the forced open-boundary tide, sparse observed-gauge complex elevations, and separate validation gauges.
/app/methods/main/solver.py: a homogeneous weak baseline.
/app/selfcheck.py: runs the solver on all visible cases and reports validation-gauge elevation RMSE only.

The inverse problem is deliberately ill-posed: friction is a spatial field, the elliptic tidal response smooths away its fine structure, and gauges are sparse, so many friction fields fit the observed gauges while disagreeing elsewhere. Additionally, a fraction of the observed gauges are faulty — they carry gross, non-Gaussian errors unrelated to the true tide — and which gauges are faulty is not disclosed. The separate validation gauges are clean.

What You Submit

Submit /app/methods/main/solver.py. It should infer a full log-friction field from each case's bathymetry, boundary forcing, observed gauge locations, and observed complex elevations. You may implement optimization, basis design, regularization, adjoint/gradient methods, ensembling, or other numerical methods inside that file.

How It Is Judged

The verifier imports your solver in a restricted child process, gives it new anonymized cases without validation heads, and uses the trusted simulator to compute complex tidal-elevation RMSE at sealed gauges. Lower RMSE is better; the score increases monotonically after clearing the disclosed weak-baseline gate of 0.14, and beating the reference solver is the goal.

Metric

mean gauge RMSE over the eight sealed basins · lower is better

RMSE of simulated vs true heads at each basin's sealed scoring gauges, via the trusted tidal simulator

	anchor	held-out	reward
B	weak homogeneous baseline (logf=-1)	0.139	0.00
R	reference solver (robust IRLS)	0.0146	0.30
S	SOTA (hard reject + CV refit)	0.007805	0.60
U	noise floor sqrt(2)*sigma	0.004243	1.00

normalisation

m >= B	`0`
B > m >= R	`0.3 * (u(m) - u(B)) / (u(R) - u(B))`
R > m >= S	`0.3 + 0.3 * (u(m) - u(R)) / (u(S) - u(R))`
S > m >= U	`0.6 + 0.4 * (u(m) - u(S)) / (u(U) - u(S))`
m < U	`1`

m = this run's held-out metric · B = weak homogeneous baseline (logf=-1) · R = reference solver (robust IRLS) · S = SOTA (hard reject + CV refit) · U = noise floor sqrt(2)*sigma

u(x) = -log10(x), so reward is piecewise-linear in decades of RMSE. Mapped per sealed basin against the four anchors, then averaged.

Rollouts

129 minwall clock

$28.15spend

44.9Mtokens

21versions, 12 kept

keptrevertedno scoreturning point

v1Inherited baseline: homogeneous logf = -1 everywhere0.1294271 min · $0.20
v2Fit one homogeneous logf, trimming the two largest gauge residuals0.042152 min · $0.30
v3Invert 8 low-frequency DCT modes: soft-L1 fit, drop two residuals, clean refitFriction is a field, not a scalar, so invert in the few smooth modes the elliptic tidal response can still resolve.0.0122514 min · $0.51
v415 DCT modes, base ridge weakened to 1e-40.01273710 min · $1.12
v525 DCT modes at base ridge 1e-40.01144815 min · $1.62
v6Cut the first-stage soft-L1 scale from 0.02 to 0.0080.01144721 min · $2.33
v7Return the converged soft-L1 field, no trimming or clean refit0.01968422 min · $2.48
v8Raise DCT rank from 25 to 350.01192432 min · $3.91
v935 KL modes from 2,000 draws of the disclosed friction priorThe generator's prior is disclosed: sample it and fit in its own eigenmodes, with the ridge scaled by eigenvalue.0.01191137 min · $4.79
v10Fall back to DCT-8 when KL and DCT disagree and gauge coverage is sparse0.01191146 min · $6.22
v11Rank 100 KL modes by prior sigma times head sensitivity, keep the top 350.01182258 min · $8.51
v12Weaken the KL ridge by 15%0.01173266 min · $10.45
v13Continuation: robust fit in 8 modes finds the outliers, clean refit in 35Naming the faulty gauges needs few modes, resolving the field needs many; screen coarse, then refit fine from it.0.01105369 min · $11.11
v14Coarse continuation rank 8 -> 40.01184875 min · $12.33
v15Run both ranks; take rank-4 only when its posterior cost is 0.8x rank-80.01105380 min · $13.41
v16Widen the goal-oriented KL basis from 35 to 50 modes0.01112588 min · $15.70
v17Order the top 50 modes per basin by finite-difference head sensitivity0.01113391 min · $16.45
v18Jacobian column scaling in every least-squares stage0.01113398 min · $18.27
v19Halve the ridge on active modes 36-50 only0.011902106 min · $20.90
v20Prescreen every second-outlier index when the second residual is small0.011125125 min · $26.43
v21Cleanup: drop the abandoned DCT and fallback paths; behaviour unchanged0.011125128 min · $27.91

21 snapshots in 129 min for $28.15. Visible six flat after v3; keeps were judged on disjoint generator seed panels, not on the six.

On the hidden set

	held-out metric	reward
weak homogeneous baseline (logf=-1)	0.139	0.00
reference solver (robust IRLS)	0.0146	0.30
SOTA (hard reject + CV refit)	0.007805	0.60
noise floor sqrt(2)*sigma	0.004243	1.00
this run	0.006911	0.7153

taskhttps://huggingface.co/datasets/autoresearch-arena/rsi-tasks-1/tree/main/tidal_friction_inverserollouthttps://huggingface.co/datasets/autoresearch-arena/rsi-rollout/tree/main/tidal_friction_inverse/codex-gpt-5.6-sol-max/tidal_friction_inverse__zEwzJRj

32 minwall clock

$5.22spend

6.3Mtokens

21versions, 12 kept

keptrevertedno scoreturning point

v0Inherited baseline: homogeneous logf = -1 everywhere0.1294271 min · $0.18
v1Fit one homogeneous logf, trimming the two largest gauge residuals12% of gauges are disclosed as faulty, so drop the two worst squared residuals before calibrating a single friction value.0.0421452 min · $0.26
v2Add 8 cosine modes through degree 2, prior widths from generator drawsGive friction spatial structure, but only as much as the generator supports: each mode's prior width is measured, not guessed.0.0152043 min · $0.36
v3Widen the basis to 15 modes through degree 30.0143474 min · $0.50
v4Weaken the coefficient-prior scale from 0.02 to 0.010.0129635 min · $0.59
v5Weaken the prior scale again to 0.0050.0121576 min · $0.68
v6Prior scale 0.00250.0131727 min · $0.78
v7Degree-4 basis (24 modes), prior widths from 2,000 generator draws0.0123729 min · $1.05
v8Prior scale 0.0075 on the degree-4 model0.01268510 min · $1.22
v9Sixth spectral band, 35 modes in total0.01243614 min · $1.71
v10Four-fold clean-gauge CV picks basis degree and prior per basinnot run on visible six17 min · $2.04
v11Double the prior penalty on the frequency-4 modes only0.0123718 min · $2.30
v1224-mode whitening prior from a 5,000-draw generator covariancePer-mode penalties assume independent generator coefficients; the covariance says otherwise, so whiten whole fields instead.0.01263521 min · $2.74
v13Whitening-prior scale 0.0040.01279521 min · $2.89
v14Whitening-prior scale 0.0060.01271223 min · $3.15
v15Mild 0.02 penalty pulling the field mean toward logf = -10.01267124 min · $3.41
v16Strengthen that global-mean penalty to 0.050.01284525 min · $3.67
v17Global-mean penalty 0.100.013126 min · $3.95
v18Bad-gauge count from the published 12% rate, one re-screen and refit0.01284528 min · $4.27
v19Try four second-outlier exclusions, keep the best training objectivenot run on visible six29 min · $4.55
v20Cleanup: drop unused prior constants; behaviour identical to v180.01284532 min · $5.03

21 snapshots in 32 min for $5.02. Keeps were decided on a 48-seed generator panel, not the visible six, where four keeps score worse than v5.

On the hidden set

	held-out metric	reward
weak homogeneous baseline (logf=-1)	0.139	0.00
reference solver (robust IRLS)	0.0146	0.30
SOTA (hard reject + CV refit)	0.007805	0.60
noise floor sqrt(2)*sigma	0.004243	1.00
this run	0.007482	0.6444

302 minwall clock

$17.37spend

21.7Mtokens

12versions, 11 kept

keptrevertedno scoreturning point

v1Adjoint Gauss-Newton: 160-mode DCT prior basis, LM damping, Tukey IRLSOne sparse LU plus an adjoint solve per gauge gives the exact PDE Jacobian, making full Gauss-Newton over 160 modes affordable.0.037188 min · $1.04
v2Hyperparameter sweep: ridge 0.02 to 1e-4, 160 to 300 modes, higher floor0.0151612 min · $1.53
v3Leave-one-out CV picks the ridge per case and flags faulty gaugesMove selection onto held-out gauges, which is what the sealed metric measures; gauges no ridge level can predict get flagged.0.0139519 min · $2.25
v4Closed-form blocked Sherman-Morrison LOO replaces refits; 8-point grid0.0136522 min · $2.73
v5Add the missing spatial-mean mode, freeing the background friction levelProjecting the true field onto the basis still scored 0.12: with no constant mode the mean friction level stayed frozen.0.0102731 min · $3.63
v6Refactor to an explicit basis argument; multi-prior candidates dropped0.0106951 min · $4.86
v7Dual-form dense algebra plus a 42 s wall-clock guard for the 2-core quota0.01025165 min · $10.51
v8Symmetric-mode sparse LU, real products; same scores, 4x faster worst case0.01025169 min · $11.16
v9Selection variants: shifted alpha, median aggregation, wider gridsall within noise177 min · $11.61
v10Multi-start over the background friction level, judged by held-out score0.00976211 min · $13.39
v11Cleanup: drop inert knobs; multi-start becomes the one selection path0.00976259 min · $15.00
v12Fail-safe config hook so a malformed SOLVER_CFG cannot raise at import0.00976283 min · $16.19

12 snapshots, $16.19 by v12. Two hours sit between v6 and v7 on runtime alone: 2-core quota while BLAS sees 96, solver calls 42-80 s against 60 s.

On the hidden set

	held-out metric	reward
weak homogeneous baseline (logf=-1)	0.139	0.00
reference solver (robust IRLS)	0.0146	0.30
SOTA (hard reject + CV refit)	0.007805	0.60
noise floor sqrt(2)*sigma	0.004243	1.00
this run	0.008031	0.6129

taskhttps://huggingface.co/datasets/autoresearch-arena/rsi-tasks-1/tree/main/tidal_friction_inverserollouthttps://huggingface.co/datasets/autoresearch-arena/rsi-rollout/tree/main/tidal_friction_inverse/claude-code-opus-5-high/tidal_friction_inverse__bxsznL5

25 minwall clock

$0.43spend

1.6Mtokens

1versions, 1 kept

No trajectory curve: this run left one comparable self-check measurement, so there is nothing to plot against spend. The versions and what each one changed are below.

v14x4 control grid bilinear-upscaled to 24x24, Cauchy loss, L2 pull, L-BFGS-BCauchy influence drops to zero on the faulty gauges, and 16 control points keep 22 observations from overfitting 576 pixels.0.01283425 min · $0.37

One snapshot in 25 min for $0.43. Loss shape, grid size, ridge and init were swept in a throwaway sandbox; only the winning config was written back.

On the hidden set

	held-out metric	reward
weak homogeneous baseline (logf=-1)	0.139	0.00
reference solver (robust IRLS)	0.0146	0.30
SOTA (hard reject + CV refit)	0.007805	0.60
noise floor sqrt(2)*sigma	0.004243	1.00
this run	0.011713	0.4633

taskhttps://huggingface.co/datasets/autoresearch-arena/rsi-tasks-1/tree/main/tidal_friction_inverserollouthttps://huggingface.co/datasets/autoresearch-arena/rsi-rollout/tree/main/tidal_friction_inverse/gemini-cli-gemini-3.7-flash-ultra/tidal_friction_inverse__M8Dmjd4