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This paper compares the results of applying a recently developed method ofstochastic uncertainty quantification designed for fluid dynamics to theBorn-Infeld model of nonlinear electromagnetism. The similarities in theresults are striking. Namely, the introduction of Stratonovich cylindricalnoise into each of their Hamiltonian formulations introduces stochastic Lietransport into their dynamics in the same form for both theories. Moreover, theresulting stochastic partial differential equations (SPDE) retain theirunperturbed form, except for an additional term representing induced Lietransport by the set of divergence-free vector fields associated with thespatial correlations of the cylindrical noise. The explanation for thisremarkable similarity lies in the method of construction of the Hamiltonian forthe Stratonovich stochastic contribution to the motion in both cases; which isdone via pairing spatial correlation eigenvectors for cylindrical noise withthe momentum map for the deterministic motion. This momentum map is responsiblefor the well-known analogy between hydrodynamics and electromagnetism. Themomentum map for the Maxwell and Born-Infeld theories of electromagnetismtreated here is the 1-form density known as the Poynting vector. Two Appendicestreat the Hamiltonian structures underlying these results.

Stochastic Evolution of Augmented Born--Infeld Equations