Transient Heat Conduction — inverse heat conduction (IHCP) L1-195

Heat TransferParabolic PDE inverse source/BC estimationδ=5 · challengingL_DAG = 3📋 Stub — not mineable

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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

r h o \cdot c p \cdot d T / d t = d i v (k g r a d T) + Q (x, t); B C s : D i r i c h l e t / N e u mann / R o bina t b o u n d a r i es

Transient Heat Conduction — inverse heat conduction (IHCP) forward model.

L-DAG

L.initial_condition -> L.parabolic_propagate -> S.record.sensors -> int.temporal

L.initial_conditionL.parabolic_propagateS.record.sensorsint.temporal

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: unstable
κ:: 800

IHCP is ill-posed (Hadamard): high-frequency BC content decays exponentially. Requires regularization (Tikhonov, future-time-stepping, PINN).

Solvability C

Solver class:: Beck-FTS, Tikhonov, PINN-IHCP
Convergence rate q:: 2
Complexity:: O(N log N) per iteration

Specs (0)

No L2 specs registered yet for this principle.