Neural operators for surrogate modeling in complex dynamic systems

Surrogate modelling is commonly used to approximate the behaviour of complex dynamic systems, especially when direct simulations are computationally expensive or impractical. Traditional methods such as reducedorder modelling and regression techniques have been effective in many contexts but often struggle to capture the nonlinearities and high-dimensionality inherent in such systems. Recent developments in neural operators, a class of deep learning models designed to approximate mappings between function spaces, offer a more flexible framework for addressing these challenges. These models are well-suited to systems governed by ordinary differential equations (ODEs), where they can model nonlinear behaviours with a high degree of accuracy. Physics-informed regularizers, which introduce a learning bias into the model, provide a mechanism for aligning the predictions of neural operators with known physical laws. This bias influences the learning process by constraining the model to produce outputs that are consistent with the underlying physical principles, thus improving the accuracy of the surrogate model. By embedding physical knowledge directly into the training process, the approach ensures that predictions remain physically plausible even in situations where the data is sparse or noisy. This paper explores the application of neural operators in surrogate modelling for magnetorheological (MR) dampers, components used in vibration control systems. MR dampers exhibit nonlinear dynamic behaviour that challenges conventional modelling techniques. The proposed approach uses neural operators to approximate the damper’s response, governed by ODEs, across a range of operating conditions. The results demonstrate that neural operators when enhanced with physics-informed regularizers, can provide accurate approximations while reducing computational cost. This approach offers a scalable alternative to traditional methods, with potential applications in real-time system control and optimization.