Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both accurate and physically interpretable remains difficult. To address this, we propose Structured Kolmogorov-Arnold Neural ODEs (SKANODEs), a framework that integrates structured state-space modeling with Kolmogorov-Arnold Networks (KANs). Within a Neural ODE architecture, SKANODE employs a fully trainable KAN as a universal function approximator to perform virtual sensing, recovering latent states that correspond to interpretable physical quantities such as displacements and velocities. Leveraging KAN's symbolic regression capability, SKANODE then extracts compact, interpretable expressions for the system's governing dynamics. Experiments on two canonical nonlinear oscillators and a real-world F-16 ground vibration dataset demonstrate that SKANODE reliably recovers physically meaningful latent displacement and velocity trajectories from acceleration measurements, identifies the correct governing nonlinearities--including the cubic stiffness in the Duffing oscillator and the nonlinear damping structure in the Van der Pol oscillator--and reveals hysteretic signatures in the F-16 interface dynamics through structured latent phase portraits and an interpretable symbolic model. Across all three cases, SKANODE provides more accurate and robust predictions than black-box NODE baselines and classical ARX and NARX identification, while producing equation-level descriptions of the learned nonlinear dynamics.

翻译：理解和建模非线性动力系统是科学与工程领域的根本性挑战。深度学习在捕捉复杂系统行为方面展现出卓越潜力，但构建兼具精度与物理可解释性的模型仍存在困难。为此，我们提出结构化Kolmogorov-Arnold神经常微分方程（SKANODEs）框架，该框架将结构化状态空间建模与Kolmogorov-Arnold网络（KANs）相结合。在神经常微分方程架构中，SKANODE采用完全可训练的KAN作为通用函数逼近器实现虚拟传感，恢复与位移、速度等可解释物理量对应的潜在状态。借助KAN的符号回归能力，SKANODE进一步提取系统控制动力学的紧凑可解释表达式。在两类经典非线性振荡器及真实F-16地面振动数据集上的实验表明：SKANODE能从加速度测量中可靠恢复具有物理意义的潜在位移与速度轨迹，正确识别控制非线性——包括Duffing振荡器中的立方刚度与Van der Pol振荡器中的非线性阻尼结构，并通过结构化潜在相图与可解释符号模型揭示F-16界面动力学中的迟滞特征。在全部三个案例中，SKANODE相比黑箱NODE基线方法及经典ARX和NARX辨识方法提供了更精确稳健的预测，同时输出学习所得非线性动力学的方程级描述。