Transfer learning for improved generalizability in causal
  physics-informed neural networks for beam simulations
Taniya Kapoor Hongrui Wang Alfredo Nunez Rolf Dollevoet
This paper introduces a novel methodology for simulating the dynamics of
beams on elastic foundations. Specifically, Euler-Bernoulli and Timoshenko beam
models on the Winkler foundation are simulated using a transfer learning
approach within a causality-respecting physics-informed neural network (PINN)
framework. 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. 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 $L^2$-norm metric and accelerating convergence.