The Rashomon Effect Meets the Butterfly Effect: Coupling Predictive Multiplicity to Chaotic Sensitivity

Uncertainty in physical-AI models is approached two ways: ensembles of retrained models sample a slice of the Rashomon set of near-equally-good models, while repeated sampling of a single generative model measures variation within one member of that set. Both miss that a model can be accurate yet violate a conservation law, and neither couples model disagreement to the physical system's own dynamics. We define a physics-constrained Rashomon set, explore it with projection-free Langevin dynamics (with a non-asymptotic convergence guarantee), and couple the sampler to the system's tangent flow through the model Jacobian and fundamental matrix. On Lorenz-96 and Kuramoto--Sivashinsky we find that physics-guided sampling halves the physical violation at $\approx 4\%$ accuracy cost, that forecast disagreement grows at the system's finite-time Lyapunov exponent, that the coupled linear theory predicts the within-chain spread up to a constant, and that epistemic and aleatoric-like disagreement trade off dominance with horizon.