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

TL;DR

This paper presents a transfer learning approach within causality-respecting physics-informed neural networks to improve the generalizability and efficiency of beam simulation models, effectively handling large domains and noisy data.

Contribution

It introduces a transfer learning methodology for causality-respecting PINNs that enhances convergence speed and accuracy in simulating beam dynamics across diverse scenarios.

Findings

Outperforms state-of-the-art PINNs in accuracy and convergence speed

Successfully handles noisy initial data in beam simulations

Extends applicability to Timoshenko beams in larger domains

Abstract

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.