The reactiondiffusion 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 reactiondiffusion 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 twodimensional onecomponent reactiondiffusion system by using machine learning. An encoderdecoder 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 timedependent behaviour of the reactiondiffusion 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 CNNbased learning model provides a rapid and accurate tool for predicting the concentration distribution of the reactiondiffusionmore »
Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic RealWorld Simulations
In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019 ; Lee et al., 2020 ). Since the quasisteadystate solutions required for fastdiffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steadystate diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speedups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could more »
 Award ID(s):
 1720625
 Publication Date:
 NSFPAR ID:
 10359456
 Journal Name:
 Frontiers in Physiology
 Volume:
 12
 ISSN:
 1664042X
 Sponsoring Org:
 National Science Foundation
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Abstract 
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