We introduce a formalism for constructing cohomological field theories (CohFTs) from nonlinear partial differential equations (PDEs). Applying this formalism to the generalized Seiberg-Witten equations, we show that the resulting CohFT functionals match those previously proposed by physicists. This provides a unified perspective on the full supersymmetric functionals of the Donaldson-Witten, Seiberg-Witten, and Kapustin-Witten theories. We also outline a quantization program for this framework and discuss its potential to produce manifold invariants and quantum cohomologies. This is joint work with Jürgen Jost.
