Active learning with neural ordinary differential equations for data-efficient modeling of tuned mass dampers

The increasing use of structural vibration control devices in civil engineering necessitates efficient data-driven modeling to support rapid design and real-time applications, including digital twins. Performance testing of tuned mass dampers (TMDs) and their variants, such as tuned liquid column dampers (TLCDs), which are widely used in engineering practice, provides an excellent basis for developing and validating such models. However, comprehensive testing remains costly and time-consuming. This study proposes an active learning framework that autonomously optimizes experimental parameters to generate the most informative training data with minimal effort. The framework employs pattern search optimization to identify optimal test conditions based on model accuracy metrics. Neural Ordinary Differential Equations (Neural ODEs) are utilized to model response data, accurately capturing nonlinearities while eliminating the need for separate restoring-force measurements. The proposed approach extends the standard Neural ODE architecture to model forced vibrations and simultaneously estimate the often-unknown modal mass, addressing a fundamental limitation in TMD identification. Experimental validation is conducted on a TLCD using a shaking table, employing harmonic excitation for training and sine-sweep excitation for model error estimation, in accordance with standard performance testing protocols. The results demonstrate that the proposed framework achieves a 90% success rate with only 20 experiments, a 43% reduction compared to the 35 experiments required by conventional unsupervised sampling methods. Robustness is further validated through broadband noise testing, confirming generalization beyond training conditions. Finally, the developed model is applied to a numerical example, demonstrating its broader applicability to structural engineering problems. • Generation of data-driven Neural ODE models from experiments. • Autonomous sampling of informative training data to save experimental effort. • Simultaneous modeling of forced vibrations and identification of modal mass. • Experimental validation using a tuned liquid column damper prototype. • Application of the obtained model to the control analysis of a structure.