Hysteresis is a nonlinear phenomenon in mechanical systems, particularly in bolted joint assemblies, where the relative motion between connected surfaces induces complex dynamic responses. Traditional methods for calibrating reduced-order models, such as the Bouc-Wen model, often rely on heuristic techniques, requiring significant domain expertise and computational resources. This research introduces a neural calibration framework utilizing neural differential equations [1] as an alternative approach within the context of physics-informed machine learning for parameter estimation in hysteresis models. The approach integrates time series data from vibration measurements with a neural network to estimate parameters governing hysteretic behavior, such as damping, stiffness, and restoring forces. The proposed method achieves predictive accuracy by embedding physical principles directly into the neural architecture while maintaining computational efficiency. The framework is validated through an experimental setup involving bolted joint assemblies subjected to varying operational conditions [2]. The results illustrate the capability of the neural model to replicate hysteresis loops and capture dynamic interactions, underscoring its potential for real-time health monitoring and diagnostics in structural systems. This novel neural calibration approach operates efficiently in real-time applications, as it processes data as it arrives, paving the way for advanced applications of machine learning in structural dynamics. [1] Gaskin, T., Pavliotis, G.A. and Girolami, M. (2023) ‘Neural parameter calibration for large-scale multiagent models’, Proceedings of the National Academy of Sciences, 120(7), p. e2216415120. Available at: https://doi.org/10.1073/pnas.2216415120. [2] Miguel, L.P., Teloli, R. de O. and da Silva, S. (2020) ‘Some practical regards on the application of the harmonic balance method for hysteresis models’, Mechanical Systems and Signal Processing, 143, p. 106842. Available at: https://doi.org/10.1016/j.ymssp.2020.106842.