Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations

This paper proposes a novel framework for simulating the dynamics of beams on elastic foundations. Specifically, partial differential equations modeling Euler–Bernoulli and Timoshenko beams on the Winkler foundation are simulated using a causal physics-informed neural network (PINN) coupled with transfer learning. Conventional PINNs encounter challenges in handling large space–time domains, even for problems with closed-form analytical solutions. A causality-respecting PINN loss function is employed to overcome this limitation, effectively capturing the underlying physics. However, it is observed that the causality-respecting PINN lacks generalizability. We propose using solutions to similar problems instead of training from scratch by employing transfer learning while adhering to causality to accelerate convergence and ensure accurate results across diverse scenarios. The primary contribution of this paper lies in introducing a causality-respecting PINN loss function in the context of structural engineering and coupling it with transfer learning to enhance the generalizability of PINNs in simulating the dynamics of beams on elastic foundations. Numerical experiments on the Euler–Bernoulli beam highlight the efficacy of the proposed approach for various initial conditions, including those with noise in the initial data. Furthermore, the potential of the proposed method is demonstrated for the Timoshenko beam in an extended spatial and temporal domain. Several comparisons suggest that the proposed method accurately captures the inherent dynamics, outperforming the state-of-the-art physics-informed methods under standard L²-norm metric and accelerating convergence.