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Sparse Observation Recovery of 2D Scalar Conservation Dynamics with Discontinuities

  • Task ID: math.sparse_hyperbolic_recovery_2d
  • Domain: math
  • Subdomain: inverse_problems
  • Status: final
  • Benchmark set: seed42 (60 tasks)
  • Tags: inverse-problems, hyperbolic-pde, discontinuity, shock-tracking, sparse-observation, rankine-hugoniot, 2d

Runtime and requirements

  • Estimated time: 60 minutes
  • Python: >=3.10
  • Packages: numpy>=1.26, scipy>=1.11, matplotlib>=3.8
  • GPU required: no
  • Network required: no

Public input and output contract

Inputs

  • data/spacetime_observations.npz (data): Scattered (t, x, y, u) observation tuples covering the spacetime domain; contains noise and uneven spatial coverage.
  • data/observation_grid.json (data): Metadata describing the observation domain extents, time range, and the evaluation timestamps at which a dense reconstruction is expected.
  • data/quantity_description.md (data): Plain-language description of what the scalar quantity represents; contains no methodological hints.

Outputs

  • analysis.py (code): End-to-end reconstruction script produced by the agent.
  • reconstructed_field.npy (data): Dense reconstruction of the scalar field on the evaluation grid, shape [n_eval_times, 128, 128], float32.
  • transition_curves.npz (data): Per-evaluation-timestep sampled points on the detected sharp-transition curves. Keys are 't_0'..'t_{n-1}', each an array of shape [M_k, 2] in (x, y) order.
  • transition_normals.npz (data): Per-evaluation-timestep outward unit normals on the detected transition curves. Same keys and M_k ordering as transition_curves.npz; each array has shape [M_k, 2].
  • transition_speeds.npz (data): Per-evaluation-timestep normal speeds of the transition curves. Same keys and ordering; each array has shape [M_k].
  • governing_model.json (data): Agent's hypothesis about the underlying dynamical law. Use `isotropic_burgers` only for the normalized case `alpha_x=alpha_y=1`; otherwise use `anisotropic_burgers` with fitted positive coefficients.
  • consistency_report.json (data): Agent-reported statistics summarising how well the detected transitions are consistent with the proposed governing model (residual quantiles, pass fraction, methodology note).
  • reconstruction_slices.png (figure): Multi-panel figure showing reconstructed field and detected discontinuity curves on representative timestamps.
  • exploration_summary.json (data): Intermediate summary of observation count, value range, noise estimate, coverage estimate, and value histogram as a list of [left_bin_edge, count] pairs.
  • transition_mask_preview.npy (data): Boolean preview mask of detected transition cells, shape [n_eval_times, 128, 128].
  • model_candidates.json (data): Intermediate list of at least two candidate flux families with motivations.
  • diagnostic_report.json (data): Intermediate per-evaluation-time RH residual diagnostics.

Public repository files

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Provenance

This task is included in the current seed42 benchmark set at dataset revision f11a199f71fb4b854ac43a1bf548d5df519141a9.

This page is generated only from files tracked in the public ASI-Bench repository at commit f18382f03faf. Submission bundles, run logs, private scoring configuration, and private reference answers are not read by this page generator.