Symbolic by Design: Zero-Prior Neural ODE Discovery via Decoupled Affine KANs

Neural scientific discovery aims to uncover governing laws from observational data, requiring models that capture underlying physical mechanisms rather than merely interpolate trajectories. For ordinary differential equations, this objective exposes a fundamental trade-off. Flexible neural function approximators accurately fit noisy dynamics but rarely recover compact symbolic equations, whereas sparse symbolic regression methods produce interpretable formulas at the cost of strong prior assumptions. We propose DA-KAN, a decoupled affine Kolmogorov-Arnold network for zero-prior differential equation discovery. DA-KAN makes symbolifiability an architectural property by representing each ODE coefficient with an explicit global affine path, which carries the recoverable symbolic law, together with an annealed local RBF residual path that absorbs optimization mismatch and noise during training. DA-KAN combines this operator with Wronskian multi-trajectory excitation, cascade order validation, and a frozen noise-agnostic adaptive extractor based on residual-checked snapping and affine projection. Extensive experiments on representative affine-coefficient ODE benchmarks demonstrate that DA-KAN achieves robust exact symbolic recovery under noisy observations without requiring the true differential order, consistently outperforming representative neural and symbolic baselines. These results indicate that embedding symbolic structure into the network architecture substantially improves exact equation recovery for zero-prior affine-coefficient ODE discovery.