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

2023/11/01 by Taniya Kapoor, Hongrui Wang, Kapoor, Taniya +5 · 3 citations
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Neural Networks and Reservoir Computing

paper · pdf · doi:10.48550/arxiv.2311.00578

openalex publication_date 2023/11/01 · openalex created_date 2023/11/03 · openalex updated_date 2026/07/28

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 L²-norm metric and accelerating convergence.

Cited by

• Domain decomposition architectures and Gauss-Newton training for physics-informed neural networks
• Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy
• Improving physics-informed neural network extrapolation via transfer learning and adaptive activation functions

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