| { |
| "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" |
| } |
|
|
|
|
