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Ill-Posed Inverse Problem Diagnosis & Multi-Method Solution

  • Task ID: math.ill_posed_inverse_problem
  • Domain: math
  • Subdomain: inverse_problems
  • Status: final
  • Benchmark set: seed42 (60 tasks)
  • Tags: ill-posed, regularization, tikhonov, tsvd, inverse-problems, colored-noise, mixed-structure, picard-plot, diagnosis, multi-method

Runtime and requirements

  • Estimated time: 45-90 minutes
  • Python:
  • Packages: numpy, scipy
  • GPU required: no
  • Network required: yes

Public input and output contract

Inputs

  • K.npy (data): Ill-conditioned matrix (n x n)
  • y_obs.csv (data): Noisy observation vector (n,) with correlated (colored) noise

Outputs

  • results/diagnosis/picard_data.csv (data): Picard plot data: singular_value, fourier_coeff, picard_ratio columns
  • results/diagnosis/diagnosis_report.md (markdown): SVD analysis, DPC judgment, noise estimate, effective rank, method recommendation
  • results/solution/tikhonov/x_reg.csv (data): Tikhonov regularized solution vector (B1/B2)
  • results/solution/tikhonov/reg_param.txt (data): Tikhonov regularization parameter lambda (B1/B2)
  • results/solution/tikhonov/lcurve_data.csv (data): L-curve data if using L-curve method (B1/B2, optional)
  • results/solution/tsvd/x_reg.csv (data): TSVD regularized solution vector (B1/B2)
  • results/solution/tsvd/reg_param.txt (data): TSVD truncation parameter k (B1/B2)
  • results/solution/cgls/x_reg.csv (data): CGLS/LSQR iterative solution vector (B1/B2, bonus)
  • results/solution/cgls/reg_param.txt (data): CGLS stopping iteration (B1/B2, bonus)
  • results/solution/method_a/x_reg.csv (data): Solution from first approach (B3/B4)
  • results/solution/method_a/reg_param.txt (data): Selected parameter for first approach (B3/B4)
  • results/solution/method_b/x_reg.csv (data): Solution from second approach (B3/B4)
  • results/solution/method_b/reg_param.txt (data): Selected parameter for second approach (B3/B4)
  • results/solution/method_c/x_reg.csv (data): Solution from third approach (B3/B4, bonus)
  • results/solution/method_c/reg_param.txt (data): Selected parameter for third approach (B3/B4, bonus)
  • results/comparison/comparison_report.md (markdown): Cross-method comparison: error, cost, suitability analysis
  • results/comparison/recommended_solution.csv (data): Recommended best solution vector for this problem
  • solution.py (code): Agent-generated self-contained solver script

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.