Physics-informed machine learning for moving load problems
This addresses simulation challenges for moving loads in structural analysis, but it is incremental as it adapts an existing PIML approach to a specific mathematical difficulty.
The paper tackled simulating moving load problems in structural engineering by approximating the Dirac delta function with a Gaussian function in physics-informed neural networks, resulting in an effective method for predicting beam deflections and load magnitudes in forward and inverse problems.
This paper presents a new approach to simulate forward and inverse problems of moving loads using physics-informed machine learning (PIML). Physics-informed neural networks (PINNs) utilize the underlying physics of moving load problems and aim to predict the deflection of beams and the magnitude of the loads. The mathematical representation of the moving load considered in this work involves a Dirac delta function, to capture the effect of the load moving across the structure. Approximating the Dirac delta function with PINNs is challenging because of its instantaneous change of output at a single point, causing difficulty in the convergence of the loss function. We propose to approximate the Dirac delta function with a Gaussian function. The incorporated Gaussian function physical equations are used in the physics-informed neural architecture to simulate beam deflections and to predict the magnitude of the load. Numerical results show that PIML is an effective method for simulating the forward and inverse problems for the considered model of a moving load.