Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics
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 introduce Holomorphic KAN-ODE, a framework that replaces the MLP with a Kolmogorov-Arnold Network (KAN) whose learnable B-spline activations reside on network edges, and incorporate...
| Authors | Bhaskar Ranjan Karn, Dinesh Kumar |
|---|---|
| Primary category | cs.LG |
| Published | 21 May 2026 |
| Last updated at source | 21 May 2026 |
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