A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation

The Poisson–Boltzmann equation (PBE) arises in various disciplines including biophysics, electrochemistry, and colloid chemistry, leading to the need for efficient and accurate simulations of PBE. However, most of the finite difference/element methods developed so far are rather complicated to imple...

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Autores principales:	In Kwon, Gwanghyun Jo, Kwang-Seong Shin
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	ResNet Poisson–Boltzmann equation deep learning machine learning immersed finite element method Electronics TK7800-8360
Acceso en línea:	https://doaj.org/article/d1523d80aee44dc79a0ffb2dc99e34d8
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spelling	oai:doaj.org-article:d1523d80aee44dc79a0ffb2dc99e34d82021-11-11T15:38:38ZA Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation10.3390/electronics102126272079-9292https://doaj.org/article/d1523d80aee44dc79a0ffb2dc99e34d82021-10-01T00:00:00Zhttps://www.mdpi.com/2079-9292/10/21/2627https://doaj.org/toc/2079-9292The Poisson–Boltzmann equation (PBE) arises in various disciplines including biophysics, electrochemistry, and colloid chemistry, leading to the need for efficient and accurate simulations of PBE. However, most of the finite difference/element methods developed so far are rather complicated to implement. In this study, we develop a ResNet-based artificial neural network (ANN) to predict solutions of PBE. Our networks are robust with respect to the locations of charges and shapes of solvent–solute interfaces. To generate train and test sets, we have solved PBE using immersed finite element method (IFEM) proposed in (Kwon, I.; Kwak, D. Y. Discontinuous bubble immersed finite element method for Poisson–Boltzmann equation. <i>Communications in Computational Physics</i> <b>2019</b>, <i>25</i>, pp. 928–946). Once the proposed ANNs are trained, one can predict solutions of PBE in almost real time by a simple substitution of information of charges/interfaces into the networks. Thus, our algorithms can be used effectively in various biomolecular simulations including ion-channeling simulations and calculations of diffusion-controlled enzyme reaction rate. The performance of the ANN is reported in the result section. The comparison between IFEM-generated solutions and network-generated solutions shows that root mean squared error are below <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>·</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></semantics></math></inline-formula>. Additionally, blow-ups of electrostatic potentials near the singular charge region and abrupt decreases near the interfaces are represented in a reasonable way.In KwonGwanghyun JoKwang-Seong ShinMDPI AGarticleResNetPoisson–Boltzmann equationdeep learningmachine learningimmersed finite element methodElectronicsTK7800-8360ENElectronics, Vol 10, Iss 2627, p 2627 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	ResNet Poisson–Boltzmann equation deep learning machine learning immersed finite element method Electronics TK7800-8360
spellingShingle	ResNet Poisson–Boltzmann equation deep learning machine learning immersed finite element method Electronics TK7800-8360 In Kwon Gwanghyun Jo Kwang-Seong Shin A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation
description	The Poisson–Boltzmann equation (PBE) arises in various disciplines including biophysics, electrochemistry, and colloid chemistry, leading to the need for efficient and accurate simulations of PBE. However, most of the finite difference/element methods developed so far are rather complicated to implement. In this study, we develop a ResNet-based artificial neural network (ANN) to predict solutions of PBE. Our networks are robust with respect to the locations of charges and shapes of solvent–solute interfaces. To generate train and test sets, we have solved PBE using immersed finite element method (IFEM) proposed in (Kwon, I.; Kwak, D. Y. Discontinuous bubble immersed finite element method for Poisson–Boltzmann equation. <i>Communications in Computational Physics</i> <b>2019</b>, <i>25</i>, pp. 928–946). Once the proposed ANNs are trained, one can predict solutions of PBE in almost real time by a simple substitution of information of charges/interfaces into the networks. Thus, our algorithms can be used effectively in various biomolecular simulations including ion-channeling simulations and calculations of diffusion-controlled enzyme reaction rate. The performance of the ANN is reported in the result section. The comparison between IFEM-generated solutions and network-generated solutions shows that root mean squared error are below <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>·</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></semantics></math></inline-formula>. Additionally, blow-ups of electrostatic potentials near the singular charge region and abrupt decreases near the interfaces are represented in a reasonable way.
format	article
author	In Kwon Gwanghyun Jo Kwang-Seong Shin
author_facet	In Kwon Gwanghyun Jo Kwang-Seong Shin
author_sort	In Kwon
title	A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation
title_short	A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation
title_full	A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation
title_fullStr	A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation
title_full_unstemmed	A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation
title_sort	deep neural network based on resnet for predicting solutions of poisson–boltzmann equation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/d1523d80aee44dc79a0ffb2dc99e34d8
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A Deep Neural Network Based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation

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