Multivariable Geometric Laplace Transform and Fault Detection in Distributed-Converter Lines

What the math gives to ML

The paper provides a transferable spatio-temporal representation: a two-variable Laplace transform in a commutative bicomplex or geometric algebra with independent temporal and spatial phase units. Its key asset is the factorization of a localized perturbation, R(s_t, s_x) = F_f(s_t) exp(-s_x x_f), which separates fault waveform from spatial location rather than mixing both effects in an ordinary temporal transform. A neural implementation could use a differentiable geometric spectral front-end for distributed sensor streams, followed by classification and localization heads. The strongest test is not only benchmark accuracy, but whether localization error follows the predicted phase-resolution law and whether spatial aliasing appears at the spatial Nyquist boundary.