Plates are key structural components, hence simulating their dynamic response under various loading conditions is important for a variety of applications, i.e. structural design and optimization. In this study, a deep learning-based Neural ODE recurrent architecture is proposed to accurately predict plate dynamics, particularly in out-of-training domains, a major challenge in machine learning. The proposed architecture leverages inherent causality and temporal sequencing to mitigate the problem of exploding and vanishing gradients. Several numerical experiments are conducted in order to validate the proposed approach, including Kirchhoff-Love plate dynamics with uncertain initial conditions. Confidence intervals for the plate deformation under different loading scenarios are also examined in an effort to quantify uncertainty. The results showcase that the proposed architecture improves the generalization capabilities of plate dynamics, enabling accurate prediction beyond the training data.

The accurate simulation of beam dynamics under various loading conditions is always a challenge in structural engineering. Physics-informed neural networks (PINNs), a deep learning-based computational method, have demonstrated effectiveness in solving complex Partial Differential Equations (PDEs) across disciplines ranging from aerospace to civil engineering. However, applying PINNS to simulate beam response across large spatial and temporal domains is challenging in terms of computational efficiency and accuracy. To address these issues, this study utilizes Separable Physics Informed Neural Networks (SPINNs) for simulating beam deformation over large domains with varying initial and loading conditions. Several numerical experiments are conducted based on fundamental beam theories, such as Euler-Bernoulli and Timoshenko. The study highlights how SPINNs leverage their separable architecture to process spatial and temporal inputs independently, thus efficiently capturing the underlying physics of complex beam dynamics. Overall, the numerical results show that the proposed approach predicts beam deformation accurately and efficiently, highlighting their potential to produce numerical solutions with reduced computational burden, enhanced stability, and improved accuracy.

Computer-aided simulations are routinely used to predict a prototype's performance. High-fidelity physics-based simulators might be computationally expensive for design and optimization, spurring the development of cheap deep-learning surrogates. The resulting surrogates often struggle to generalize and predict novel scenarios beyond their training domain. We propose a two-stage methodology addressing the challenge of generalization. It employs physics-based simulators, supplemented with ordinary differential equations integrated into the recurrent architecture, to learn the intrinsic dynamics. The proposed approach captures the inherent causality and generalizes the dynamics irrespective of a data source. The presented numerical experiments encompass five fundamental structural engineering scenarios, including beams on Winkler foundations based on Euler-Bernoulli and Timoshenko theories, beams under moving loads, and catenary-pantograph interactions in railways. The proposed methodology outperforms conventional recurrent methods and remains invariant to data sources, showcasing its efficacy. Numerical experiments highlight its prospects for design optimization, predictive maintenance, and enhancing safety measures.