Advection-Dispersion Transport Inversion L1-415
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
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Forward model E
Advection-Dispersion Transport Inversion: ADE inversion: recover solute source concentration history from downgradient breakthrough curves. The forward operator produces the measurement through a 3-node primitive DAG (M.ade.advection_dispersion…); recovery is posed as a linear_inverse problem. Difficulty tier delta=3 with effective condition number kappa_eff~200; velocity_field_uncertainty, dispersion_coefficient_uncertainty set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 5000
Existence of the recovered 1D_concentration_source is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 200); velocity_field_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- classical [Tikhonov_regularization or TSVD_source_inversion]
- Convergence rate q:
- 2
- Complexity:
- O(N_wells * N_timesteps * N_source_bins) for design matrix per iteration