Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics
arXiv:2605.22235v1 Announce Type: new Abstract: 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 fra
The continuous evolution of neural network architectures and the increasing demand for interpretable AI models, especially for complex systems, is driving this development.
This research introduces a novel, interpretable neural network architecture that can accurately model complex dynamical systems, potentially leading to breakthroughs in scientific discovery and engineering.
The development of Holomorphic KAN-ODE offers a new paradigm for building physically-informed AI models that respect complex-analytic geometry, moving beyond opaque black-box approaches.
- · AI researchers in complex systems
- · Scientific discovery platforms
- · Engineering simulation and design
- · Deep learning framework developers
- · Traditional black-box Neural ODE applications
- · Methods lacking interpretability in complex dynamics
Holomorphic KAN-ODE provides a more accurate and interpretable way to model systems with underlying complex-analytic dynamics.
This could accelerate the discovery of governing equations in fields like physics, biology, and chemistry by making AI models more transparent.
The principle of embedding complex-analytic priors into neural networks might inspire new architectures for other domains requiring specific mathematical properties.
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Read at arXiv cs.LG