AI RESEARCH
Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics
arXiv CS.LG
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ArXi:2605.22235v1 Announce Type: new Complex dynamical systems governed by holomorphic maps such as $z^2 + c$ exhibit fractal boundaries with extreme sensitivity to initial conditions. Accurately modelling these structures from data requires methods that respect the underlying complex-analytic geometry, yet Multi-Layer Perceptrons (MLPs) within Neural Ordinary Differential Equations (Neural ODEs) lack complex-analytic priors, violate the Cauchy--Riemann conditions, and function as opaque approximators incapable of yielding governing equations. We.