# Physics-informed machine learning for moving load problems

arXiv: https://arxiv.org/abs/2304.00369 · HTML: https://mlsanity.com/paper/2304.00369/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 16 references that are in the map.
- First posted on arXiv 1 Apr 2023.

## Builds on (most cited first, 1 of 1)

- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)

## Built on by (most cited first, 4 of 4)

- [Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations](https://mlsanity.com/paper/2311.00578/) (2023)
- [A Domain-adaptive Physics-informed Neural Network for Inverse Problems of Maxwell's Equations in Heterogeneous Media](https://mlsanity.com/paper/2308.06436/) (2023)
- [A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam](https://mlsanity.com/paper/2601.00866/) (2025)
- [Physics-Informed Neural Networks and Radial Basis Functions for PDEs with Dirac Delta Sources](https://mlsanity.com/paper/2606.12735/) (2026)

## Abstract (arXiv)

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.