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The reaction-diffusion system is naturally used in chemistry to represent substances reacting and diffusing over the spatial domain. Its solution illustrates the underlying process of a chemical reaction and displays diverse spatial patterns of the substances. Numerical methods like finite element method (FEM) are widely used to derive the approximate solution for the reaction-diffusion system. However, these methods require long computation time and huge computation resources when the system becomes complex. In this paper, we study the physics of a two-dimensional one-component reaction-diffusion system by using machine learning. An encoder-decoder based convolutional neural network (CNN) is designed and trained to directly predict the concentration distribution, bypassing the expensive FEM calculation process. Different simulation parameters, boundary conditions, geometry configurations and time are considered as the input features of the proposed learning model. In particular, the trained CNN model manages to learn the time-dependent behaviour of the reaction-diffusion system through the input time feature. Thus, the model is capable of providing concentration prediction at certain time directly with high test accuracy (mean relative error <3.04%) and 300 times faster than the traditional FEM. Our CNN-based learning model provides a rapid and accurate tool for predicting the concentration distribution of the reaction-diffusion system.

 

Abstract Neurons exhibit complex geometry in their branched networks of neurites which is essential to the function of individual neuron but also brings challenges to transport a wide variety of essential materials throughout their neurite networks for their survival and function. While numerical methods like isogeometric analysis (IGA) have been used for modeling the material transport process via solving partial differential equations (PDEs), they require long computation time and huge computation resources to ensure accurate geometry representation and solution, thus limit their biomedical application. Here we present a graph neural network (GNN)-based deep learning model to learn the IGA-based material transport simulation and provide fast material concentration prediction within neurite networks of any topology. Given input boundary conditions and geometry configurations, the well-trained model can predict the dynamical concentration change during the transport process with an average error less than 10% and $$120 \sim 330$$ 120 ∼ 330 times faster compared to IGA simulations. The effectiveness of the proposed model is demonstrated within several complex neurite networks. 

Surpervoxels are becoming increasingly popular in many point cloud processing applications. However, few methods have been devised specifically for generating compact supervoxels from unstructured three-dimensional (3D) point clouds. In this study, we aimed to generate high quality over-segmentation of point clouds. We propose a merge-swap optimization framework that solves any supervoxel generation problem formulated in energy minimization. In particular, we tailored an energy function that explicitly encourages regular and compact supervoxels with adaptive size control considering local geometric information of point clouds. We also provide two acceleration techniques to reduce the computational overhead. The performance of the proposed merge-swap optimization approach is superior to that of previous work in terms of thorough optimization, computational efficiency, and practical applicability to incorporating control of other properties of supervoxels. The experiments show that our approach produces supervoxels with better segmentation quality than two state-of-the-art methods on three public datasets.