  We introduce a formalism for constructing cohomological field theories
(CohFT) out of nonlinear PDEs based on the first author's previous work
(arXiv:2202.12425). We apply the formalism to the generalized Seiberg-Witten
equations and show that the obtained CohFT functionals agree with the existing
ones proposed by physicists. This leads to a unified perspective from which to
view the full supersymmetric functionals of the Donaldson-Witten,
Seiberg-Witten, and Kapustin-Witten theories and understand the relations
between them. We also outline a quantization program for our framework and
discuss its potential to produce manifold invariants and quantum cohomologies.
