Haotian Feng

Haotian Feng, Sabarinathan P Subramaniyan, Hridyesh Tewani et al.

Woven fabrics play an essential role in everyday textiles for clothing/sportswear, water filtration, and retaining walls, to reinforcements in stiff composites for lightweight structures like aerospace, sporting, automotive, and marine industries. Several possible combinations of weave patterns and material choices, which comprise weave architecture, present a challenging question about how they could influence the physical and mechanical properties of woven fabrics and reinforced structures. In this paper, we present a novel Physics-Constrained Neural Network (PCNN) to predict the mechanical properties like the modulus of weave architectures and the inverse problem of predicting pattern/material sequence for a design/target modulus value. The inverse problem is particularly challenging as it usually requires many iterations to find the appropriate architecture using traditional optimization approaches. We show that the proposed PCNN can effectively predict weave architecture for the desired modulus with higher accuracy than several baseline models considered. We present a feature-based optimization strategy to improve the predictions using features in the Grey Level Co-occurrence Matrix (GLCM) space. We combine PCNN with this feature-based optimization to discover near-optimal weave architectures to facilitate the initial design of weave architecture. The proposed frameworks will primarily enable the woven composite analysis and optimization process, and be a starting point to introduce Knowledge-guided Neural Networks into the complex structural analysis.

Derek Ho, Haotian Feng

The widespread distribution of microplastics (MPs) in the environment presents significant challenges for their detection and identification. Fluorescence imaging has emerged as a promising technique for enhancing plastic particle detectability and enabling accurate classification based on fluorescence behavior. However, conventional segmentation techniques face limitations, including poor signal-to-noise ratio, inconsistent illumination, thresholding difficulties, and false positives from natural organic matter (NOM). To address these challenges, this study introduces the Fluorescence Imaging Microplastic Analysis Platform (FIMAP), a retrofitted multispectral camera with four optical filters and five excitation wavelengths. FIMAP enables comprehensive characterization of the fluorescence behavior of ten Nile Red-stained MPs: HDPE, LDPE, PP, PS, EPS, ABS, PVC, PC, PET, and PA, while effectively excluding NOM. Using K-means clustering for robust segmentation (Intersection over Union = 0.877) and a 20-dimensional color coordinate multivariate nearest neighbor approach for MP classification (>3.14 mm), FIMAP achieves 90% precision, 90% accuracy, 100% recall, and an F1 score of 94.7%. Only PS was occasionally misclassified as EPS. For smaller MPs (35-104 microns), classification accuracy declined, likely due to reduced stain sorption, fewer detectable pixels, and camera instability. Integrating FIMAP with higher-magnification instruments, such as a microscope, may enhance MP identification. This study presents FIMAP as an automated, high-throughput framework for detecting and classifying MPs across large environmental sample volumes.

Haotian Feng

Reaction-diffusion systems represent one of the most fundamental formulations used to describe a wide range of physical, chemical, and biological processes. With the increasing adoption of neural networks, recent research has focused on solving differential equations using machine learning techniques. However, the theoretical foundation explaining why neural networks can effectively approximate such solutions remains insufficiently explored. This paper provides a theoretical analysis of the approximation power of neural networks for one- and two-dimensional reaction-diffusion equations in both homogeneous and heterogeneous media. Building upon the universal approximation theorem, we demonstrate that a two-layer neural network can approximate the one-dimensional reaction-diffusion equation, while a three-layer neural network can approximate its two-dimensional counterpart. The theoretical framework presented here can be further extended to elliptic and parabolic equations. Overall, this work highlights the expressive power of neural networks in approximating solutions to reaction-diffusion equations and related PDEs, providing a theoretical foundation for neural network-based differential equation solvers.

Haotian Feng, Pavana Prabhakar

Stress analysis of heterogeneous media, like composite materials, using Finite Element Analysis (FEA) has become commonplace in design and analysis. However, determining stress distributions in heterogeneous media using FEA can be computationally expensive in situations like optimization and multi-scaling. To address this, we utilize Deep Learning for developing a set of novel Difference-based Neural Network (DiNN) frameworks based on engineering and statistics knowledge to determine stress distribution in heterogeneous media, for the first time, with special focus on discontinuous domains that manifest high stress concentrations. The novelty of our approach is that instead of directly using several FEA model geometries and stresses as inputs for training a Neural Network, as typically done previously, we focus on highlighting the differences in stress distribution between different input samples for improving the accuracy of prediction in heterogeneous media. We evaluate the performance of DiNN frameworks by considering different types of geometric models that are commonly used in the analysis of composite materials, including volume fraction and spatial randomness. Results show that the DiNN structures significantly enhance the accuracy of stress prediction compared to existing structures, especially for composite models with random volume fraction when localized high stress concentrations are present.