Applications of Scientific Machine Learning for the Analysis of Functionally Graded Porous Beams

TL;DR

This paper explores and compares three Scientific Machine Learning methods—PINN, DEM, and Neural Operators—for analyzing functionally graded porous beams, demonstrating their effectiveness in predicting beam responses under various conditions.

Contribution

It introduces a unified framework applying SciML techniques to FG porous beams, including a trained neural operator capable of predicting responses for arbitrary conditions.

Findings

Neural operator accurately predicts beam responses under various porosity and traction conditions.

The methods are validated against analytical and numerical solutions, confirming their reliability.

The study provides open-source code and data for further research.

Abstract

This study investigates different Scientific Machine Learning (SciML) approaches for the analysis of functionally graded (FG) porous beams and compares them under a new framework. The beam material properties are assumed to vary as an arbitrary continuous function. The methods consider the output of a neural network/operator as an approximation to the displacement fields and derive the equations governing beam behavior based on the continuum formulation. The methods are implemented in the framework and formulated by three approaches: (a) the vector approach leads to a Physics-Informed Neural Network (PINN), (b) the energy approach brings about the Deep Energy Method (DEM), and (c) the data-driven approach, which results in a class of Neural Operator methods. Finally, a neural operator has been trained to predict the response of the porous beam with functionally graded material under any porosity distribution pattern and any arbitrary traction condition. The results are validated with analytical and numerical reference solutions. The data and code accompanying this manuscript will be publicly available at https://github.com/eshaghi-ms/DeepNetBeam.