Physics-guided Bayesian neural networks by ABC-SS: Application to reinforced concrete columns

Abstract

This manuscript proposes a physics-guided Bayesian neural network, which combines Approximate-Bayesian-Computation training with physics-based models. This hybrid algorithm uses the laws of physics to mitigate the lack of data, and the flexibility of neural networks to model the complexities inherent in nature. The state-of-the-art approaches often introduce the physics in the loss function, or through some known boundary conditions, and then use backpropagation to adjust the weights. However, this training method involves some rigidity and drawbacks, mostly related to the adoption of a predefined loss/likelihood function and the evaluation of its gradient during training. The use of approximate Bayesian computation as the learning engine results in a greater prediction accuracy and flexibility to quantify the uncertainty, due to the gradient-free nature of the algorithm, the absence of loss/likelihood function and the non-parametric formulation of the weights. Furthermore, the physics-based model is introduced in the forward pass of the neural network, which significantly increases the extrapolation capabilities of the proposed hybrid model. The proposed algorithm has been applied to lateral-load tests in reinforced concrete columns, providing promising results when making predictions about future loading cycles, surpassing the purely data-driven and physics-based methods as well as the state-of-the-art physics-guided neural networks. In light of the performance shown during the experiments, the proposed algorithm has the potential to become a useful tool for fast evaluation of critical buildings after seismic events.