We establish the large deviation principle for a sequence of stochastic PDEs defined on rescaled lattices. They are a special class of the Ginzburg-Landau models where the total order parameters is conserved. As the lattice mesh size and the magnitude of randomness go to zero, the large deviation result gives us information about convergence from the stochastic dynamic to the most probable deterministic trajectory, as well as the rate of deviations of the dynamic frorn atypical deterministic trajectories. We prove such large deviation result by using Hamilton - Jacobi equation techniques. A technical core in such a method is the comparison between sub and super (viscosity) solutions for a class of first order Hamilton - Jacobi equations. The state space for these equations is a Hilbert space, and the Hamiltonian admits a special form to which available comparison results cannot be directly applied. We obtain the large deviation result by clarifying different notions of viscosity solutions, and by extending existing comparison techniques. It is the hope that the techniques and connections revealed here will prove to be useful in further investigations of the interactions between infinite dimensional viscosity solution method and the large deviation for stochastic PDEs and interacting particle systems.

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