{
  "agent_view_tokens": 5000,
  "emoji": "🌊",
  "paper": {
    "arxiv_id": "2605.31127"
  },
  "revision": "1785142800000000000",
  "root": {
    "children": [
      {
        "children": [],
        "file": "pages/executive-summary/page.md",
        "slug": "executive-summary",
        "title": "Executive summary"
      },
      {
        "children": [],
        "file": "pages/claim-1-source-identification/page.md",
        "slug": "claim-1-source-identification",
        "title": "Claim 1: On the paper's 36 x 36 two-source advection-diffusion inverse problem with 12 noisy monitoring wells, GP-FVM reconstructs the nonparametric source field with source RMSE about 0.44 in under 2 seconds (Section 4.1 and Appendix B.1)."
      },
      {
        "children": [],
        "file": "pages/claim-2-mixed-state/page.md",
        "slug": "claim-2-mixed-state",
        "title": "Claim 2: The source-identification GP-FVM executes a joint Gaussian state over concentration values, exact face and derivative-face integrals, source values, and source cell integrals, with 8,857 variables, 1,225 finite-volume balance equations, and 141 boundary equations on the released 36 x 36 grid (Appendix B.1)."
      },
      {
        "children": [],
        "file": "pages/claim-3-uncertainty/page.md",
        "slug": "claim-3-uncertainty",
        "title": "Claim 3: On the released source-identification system, posterior concentration uncertainty collapses at the prescribed left Dirichlet boundary and contracts at the 12 measurement locations; source uncertainty is also reduced by those observations (Section 4.1)."
      },
      {
        "children": [],
        "file": "pages/claim-4-dense-convergence/page.md",
        "slug": "claim-4-dense-convergence",
        "title": "Claim 4: For the paper's dense Bayesian-quadrature GP-FVM Poisson study over N = 10, 20, 40, 80, 160, the measured convergence rates increase with Matern smoothness, reaching about 2.00, 2.71, and 3.78 for Matern-3/2, 5/2, and 7/2 (Figure 4)."
      },
      {
        "children": [],
        "file": "pages/claim-5-sparse-convergence/page.md",
        "slug": "claim-5-sparse-convergence",
        "title": "Claim 5: For the paper's sparse Poisson study at fixed rho = 5 over N = 10, 20, 40, 80, 160, Matern-3/2 preserves a convergence rate near 2 while smoother kernels plateau at fine resolution (Figure 4)."
      },
      {
        "children": [],
        "file": "pages/claim-6-ordering/page.md",
        "slug": "claim-6-ordering",
        "title": "Claim 6: On the paper's 35 x 35 mixed-functional experiment across rho in {1, 1.5, 2, 2.5, 3, 4, 5, 7, 10}, placing integrals as the coarsest block Pareto-dominates placing evaluations as the coarsest block in fill percentage and KL divergence (Appendix A.3 and Figure 6)."
      },
      {
        "children": [],
        "file": "pages/conclusion/page.md",
        "slug": "conclusion",
        "title": "Conclusion"
      }
    ],
    "file": "pages/index.md",
    "slug": "index",
    "title": "Reproduction: Scalable Bayesian Inference for Nonlinear Conservation Laws"
  },
  "schema_version": 1,
  "space_id": "ProCreations/repro-gp-finite-volume",
  "tags": [
    "icml2026-repro",
    "paper-Xg12D1Y4H1"
  ],
  "title": "Reproduction: Scalable Bayesian Inference for Nonlinear Conservation Laws",
  "updated_at": "2026-07-27T10:20:00+00:00"
}