Pub Date : 2023-09-05DOI: 10.3389/fams.2023.1272392
Ivo Siekmann, James M. Osborne
{"title":"Editorial: Do individuals matter? - Individual-based versus population-based models applied to biology and health","authors":"Ivo Siekmann, James M. Osborne","doi":"10.3389/fams.2023.1272392","DOIUrl":"https://doi.org/10.3389/fams.2023.1272392","url":null,"abstract":"","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47027801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-31DOI: 10.3389/fams.2023.1244490
Sisay Ketema Tesfaye, G. Duressa, M. Woldaregay, T. G. Dinka
A uniformly convergent numerical scheme is proposed to solve a singularly perturbed convection-diffusion problem with a large time delay. The diffusion term of the problem is multiplied by a perturbation parameter, ε. For a small ε, the problem exhibits a boundary layer, which makes it challenging to solve it analytically or using standard numerical methods. As a result, the backward Euler scheme is applied in the temporal direction. Non-symmetric finite difference schemes are applied for approximating the first-order derivative terms, and a higher-order finite difference method is applied for approximating the second-order derivative term. Furthermore, an exponential fitting factor is computed and induced in the difference scheme to handle the effect of the small parameter. Using the discrete maximum principle, the stability of the scheme is examined and analyzed. The developed scheme is parameter-uniform with a linear order of convergence in both space and time. To examine the accuracy of the method, two model examples are considered. Further, the boundary layer behavior of the solutions is given graphically.
{"title":"Fitted computational method for singularly perturbed convection-diffusion equation with time delay","authors":"Sisay Ketema Tesfaye, G. Duressa, M. Woldaregay, T. G. Dinka","doi":"10.3389/fams.2023.1244490","DOIUrl":"https://doi.org/10.3389/fams.2023.1244490","url":null,"abstract":"A uniformly convergent numerical scheme is proposed to solve a singularly perturbed convection-diffusion problem with a large time delay. The diffusion term of the problem is multiplied by a perturbation parameter, ε. For a small ε, the problem exhibits a boundary layer, which makes it challenging to solve it analytically or using standard numerical methods. As a result, the backward Euler scheme is applied in the temporal direction. Non-symmetric finite difference schemes are applied for approximating the first-order derivative terms, and a higher-order finite difference method is applied for approximating the second-order derivative term. Furthermore, an exponential fitting factor is computed and induced in the difference scheme to handle the effect of the small parameter. Using the discrete maximum principle, the stability of the scheme is examined and analyzed. The developed scheme is parameter-uniform with a linear order of convergence in both space and time. To examine the accuracy of the method, two model examples are considered. Further, the boundary layer behavior of the solutions is given graphically.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48910337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-31DOI: 10.3389/fams.2023.1224891
F. Legesse, Koya Purnachandra Rao, T. Keno
The global impact of exclusive versus inclusive nursing on particular baby mortalities and morbidities from conception to 6 months is examined in this study. Exclusive breastfeeding practices are more crucial and effective in preventing illness outbreaks when there is no access to appropriate medications or vaccinations. Additionally, this study takes optimal control theory into account, applying it to a system of differential equations that uses Pontryagin's Maximum Principle to describe a bimodal pneumonia transmission behavior in a vulnerable compartment. The proposed pneumonia transmission model was then updated to include two control variables. These include preventing illness exposure in susceptible children through various preventative measures and treating infected children through antibiotics, hospital care, and other treatments. If the threshold number (ℜ0) is less than one, then treatment and prevention rates are increased, and the disease will be wiped out of the population. However, when (ℜ0) is greater than one, then the disease persists in the population, which indicates that prevention and treatment rates are low. To evaluate the cost-effectiveness of all potential control techniques and their combinations, the incremental cost-effectiveness ratio (ICER) was determined. The simulation results of the identified model show that the interventions of prevention and treatment scenarios were the most successful in eradicating the dynamics of the pneumonia disease's propagation during the epidemic, but they were ineffective from a cost-saving perspective. Therefore, limiting pneumonia transmission to prevention alone during an outbreak is the most economical course of action.
{"title":"Cost effectiveness and optimal control analysis for bimodal pneumonia dynamics with the effect of children's breastfeeding","authors":"F. Legesse, Koya Purnachandra Rao, T. Keno","doi":"10.3389/fams.2023.1224891","DOIUrl":"https://doi.org/10.3389/fams.2023.1224891","url":null,"abstract":"The global impact of exclusive versus inclusive nursing on particular baby mortalities and morbidities from conception to 6 months is examined in this study. Exclusive breastfeeding practices are more crucial and effective in preventing illness outbreaks when there is no access to appropriate medications or vaccinations. Additionally, this study takes optimal control theory into account, applying it to a system of differential equations that uses Pontryagin's Maximum Principle to describe a bimodal pneumonia transmission behavior in a vulnerable compartment. The proposed pneumonia transmission model was then updated to include two control variables. These include preventing illness exposure in susceptible children through various preventative measures and treating infected children through antibiotics, hospital care, and other treatments. If the threshold number (ℜ0) is less than one, then treatment and prevention rates are increased, and the disease will be wiped out of the population. However, when (ℜ0) is greater than one, then the disease persists in the population, which indicates that prevention and treatment rates are low. To evaluate the cost-effectiveness of all potential control techniques and their combinations, the incremental cost-effectiveness ratio (ICER) was determined. The simulation results of the identified model show that the interventions of prevention and treatment scenarios were the most successful in eradicating the dynamics of the pneumonia disease's propagation during the epidemic, but they were ineffective from a cost-saving perspective. Therefore, limiting pneumonia transmission to prevention alone during an outbreak is the most economical course of action.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45846291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-30DOI: 10.3389/fams.2023.1238497
Fahad Al Basir
Mosaic disease in Jatropha curcas plants is caused by begomoviruses carried by whitefly vectors, and only mature vectors can transmit the virus. In this study, a mathematical model is developed for the dynamic analysis of the spread of mosaic disease in the J. curcas plantation, accounting for the whitefly maturation period as a time delay factor. The existence conditions and stability of the equilibrium points have been studied with qualitative theory. The basic reproduction number, R0, is determined to study the stability of the disease-free equilibrium with respect to it. Transcritical bifurcation of the disease-free equilibrium and Hopf bifurcation of the endemic equilibrium are also analyzed. Using numerical simulations, the analytical findings are verified and discussed the different dynamical behaviors of the system. In this research, the stabilizing role of maturation delay has been established. That means when maturation time is large, disease will be transmitted when the infection rate is high.
{"title":"Role of the whitefly maturation period on mosaic disease propagation in Jatropha curcas plant","authors":"Fahad Al Basir","doi":"10.3389/fams.2023.1238497","DOIUrl":"https://doi.org/10.3389/fams.2023.1238497","url":null,"abstract":"Mosaic disease in Jatropha curcas plants is caused by begomoviruses carried by whitefly vectors, and only mature vectors can transmit the virus. In this study, a mathematical model is developed for the dynamic analysis of the spread of mosaic disease in the J. curcas plantation, accounting for the whitefly maturation period as a time delay factor. The existence conditions and stability of the equilibrium points have been studied with qualitative theory. The basic reproduction number, R0, is determined to study the stability of the disease-free equilibrium with respect to it. Transcritical bifurcation of the disease-free equilibrium and Hopf bifurcation of the endemic equilibrium are also analyzed. Using numerical simulations, the analytical findings are verified and discussed the different dynamical behaviors of the system. In this research, the stabilizing role of maturation delay has been established. That means when maturation time is large, disease will be transmitted when the infection rate is high.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49414219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-24DOI: 10.3389/fams.2023.1216331
G. Byrenheid, S. Stasyuk, T. Ullrich
In this article, we study the sampling recovery problem for certain relevant multivariate function classes on the cube [0, 1]d, which are not compactly embedded into L∞([0,1]d). Recent tools relating the sampling widths to the Kolmogorov or best m-term trigonometric widths in the uniform norm are therefore not applicable. In a sense, we continue the research on the small smoothness problem by considering limiting smoothness in the context of Besov and Triebel-Lizorkin spaces with dominating mixed regularity such that the sampling recovery problem is still relevant. There is not much information available on the recovery of such functions except for a previous result by Oswald in the univariate case and Dinh Dũng in the multivariate case. As a first step, we prove the uniform boundedness of the ℓp-norm of the Faber coefficients at a fixed level by Fourier analytic means. Using this, we can control the error made by a (Smolyak) truncated Faber series in Lq([0,1]d) with q <∞. It turns out that the main rate of convergence is sharp. Thus, we obtain results also for S1,∞1F([0,1]d), a space “close” to S11W([0,1]d), which is important in numerical analysis, especially numerical integration, but has rather poor Fourier analytical properties.
{"title":"Lp-Sampling recovery for non-compact subclasses of L∞","authors":"G. Byrenheid, S. Stasyuk, T. Ullrich","doi":"10.3389/fams.2023.1216331","DOIUrl":"https://doi.org/10.3389/fams.2023.1216331","url":null,"abstract":"In this article, we study the sampling recovery problem for certain relevant multivariate function classes on the cube [0, 1]d, which are not compactly embedded into L∞([0,1]d). Recent tools relating the sampling widths to the Kolmogorov or best m-term trigonometric widths in the uniform norm are therefore not applicable. In a sense, we continue the research on the small smoothness problem by considering limiting smoothness in the context of Besov and Triebel-Lizorkin spaces with dominating mixed regularity such that the sampling recovery problem is still relevant. There is not much information available on the recovery of such functions except for a previous result by Oswald in the univariate case and Dinh Dũng in the multivariate case. As a first step, we prove the uniform boundedness of the ℓp-norm of the Faber coefficients at a fixed level by Fourier analytic means. Using this, we can control the error made by a (Smolyak) truncated Faber series in Lq([0,1]d) with q <∞. It turns out that the main rate of convergence is sharp. Thus, we obtain results also for S1,∞1F([0,1]d), a space “close” to S11W([0,1]d), which is important in numerical analysis, especially numerical integration, but has rather poor Fourier analytical properties.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46072108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-24DOI: 10.3389/fams.2023.1045108
H. Morofuji, S. Kurahashi
This study aims to analyze the structure of the emergence and maintenance of the cartel mechanism as an informal organization and the measures to deter bid-rigging. We propose an agent-based bid-rigging norms model and validate it with a mathematical model. We clarify that the auction system primarily used in public procurements has a structure inducing bid-rigging in which meta-norms are unnecessary. We also show that punishment for deviation from bid-rigging plays a critical role in establishing and maintaining it. In addition, we explore the authorities' actions to deter bid-rigging by examining three measures: the flexible setting of reserve prices, the administrative surcharge and leniency system under the Antimonopoly Law, and applying the bid-rigging offense under the Criminal Law. As a result, the study reveals that the administrative surcharge and the leniency system are insufficient to deter bid-rigging, and the adequate measures are the flexible setting of reserve prices and applying the bid-rigging offense. Furthermore, the simultaneous implementation of these three measures more effectively enables deterring bid-rigging.
{"title":"Carrot or stick? A study on “bid-rigging norms” by simulation: inducing factors and deterring measures","authors":"H. Morofuji, S. Kurahashi","doi":"10.3389/fams.2023.1045108","DOIUrl":"https://doi.org/10.3389/fams.2023.1045108","url":null,"abstract":"This study aims to analyze the structure of the emergence and maintenance of the cartel mechanism as an informal organization and the measures to deter bid-rigging. We propose an agent-based bid-rigging norms model and validate it with a mathematical model. We clarify that the auction system primarily used in public procurements has a structure inducing bid-rigging in which meta-norms are unnecessary. We also show that punishment for deviation from bid-rigging plays a critical role in establishing and maintaining it. In addition, we explore the authorities' actions to deter bid-rigging by examining three measures: the flexible setting of reserve prices, the administrative surcharge and leniency system under the Antimonopoly Law, and applying the bid-rigging offense under the Criminal Law. As a result, the study reveals that the administrative surcharge and the leniency system are insufficient to deter bid-rigging, and the adequate measures are the flexible setting of reserve prices and applying the bid-rigging offense. Furthermore, the simultaneous implementation of these three measures more effectively enables deterring bid-rigging.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48362170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-16DOI: 10.3389/fams.2023.1225137
Daniel J. Coffield, A. Spagnuolo, Ryan Capouellez, G. Stryker
Chagas disease has been the target of widespread control programs, primarily through residual insecticide treatments. However, in some regions like the Gran Chaco, these efforts have failed to sufficiently curb the disease. Vector reinfestation into homes and vector resistance to insecticides are possible causes of the control failure. This work proposes a mathematical model for the dynamics of Chagas disease in neighboring rural villages of the Gran Chaco region, incorporating human travel between the villages, passive vector migration, and insecticide resistance. Computational simulations across a wide variety of scenarios are presented. The simulations reveal that the effects of human travel and passive vector migration are secondary and unlikely to play a significant role in the overall dynamics, including the number of human infections. The numerical results also show that insecticide resistance causes a notable increase in infections and is an especially important source of reinfestation when spraying stops. The results suggest that control strategies related to migration and travel between the villages are unlikely to yield meaningful benefit and should instead focus on other reinfestation sources like domestic foci that survive insecticide spraying or sylvatic foci.
{"title":"A mathematical model for Chagas disease transmission with neighboring villages","authors":"Daniel J. Coffield, A. Spagnuolo, Ryan Capouellez, G. Stryker","doi":"10.3389/fams.2023.1225137","DOIUrl":"https://doi.org/10.3389/fams.2023.1225137","url":null,"abstract":"Chagas disease has been the target of widespread control programs, primarily through residual insecticide treatments. However, in some regions like the Gran Chaco, these efforts have failed to sufficiently curb the disease. Vector reinfestation into homes and vector resistance to insecticides are possible causes of the control failure. This work proposes a mathematical model for the dynamics of Chagas disease in neighboring rural villages of the Gran Chaco region, incorporating human travel between the villages, passive vector migration, and insecticide resistance. Computational simulations across a wide variety of scenarios are presented. The simulations reveal that the effects of human travel and passive vector migration are secondary and unlikely to play a significant role in the overall dynamics, including the number of human infections. The numerical results also show that insecticide resistance causes a notable increase in infections and is an especially important source of reinfestation when spraying stops. The results suggest that control strategies related to migration and travel between the villages are unlikely to yield meaningful benefit and should instead focus on other reinfestation sources like domestic foci that survive insecticide spraying or sylvatic foci.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48725760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-09DOI: 10.3389/fams.2023.1210404
Meshal Shutaywi, Ziad Ur Rehman, Z. Shah, N. Vrinceanu, Rashid Jan, Wejdan Deebani, O. Dumitrașcu
Social media addiction (SMA) is the excessive use of social media platforms, resulting in negative consequences for individuals. It is characterized by an uncontrollable urge to use social media, leading to negative effects in human's life. This study aims to construct a mathematical model to conceptualize the transmission dynamics of SMA and explore the underlying mechanisms of this harmful addiction in the framework of fractional derivative. The fundamentals of fractional calculus are listed for examining the model. Equilibrium points are identified, and the reproduction parameter R0 is computed to understand the dynamics of SMA spread. Stability analysis of the equilibria is performed, and the impact of various input parameters is numerically investigated. The existence and uniqueness of the proposed SMA model are demonstrated through simulations, which also study the intricate dynamics with respect to different input factors. To develop effective control strategies, the system's dynamical behavior is examined, and the influence of fractional derivative order on fluctuations is explored. This research offers a range of suggestions aimed at reducing the occurrence of social media addiction.
{"title":"Modeling and analysis of the addiction of social media through fractional calculus","authors":"Meshal Shutaywi, Ziad Ur Rehman, Z. Shah, N. Vrinceanu, Rashid Jan, Wejdan Deebani, O. Dumitrașcu","doi":"10.3389/fams.2023.1210404","DOIUrl":"https://doi.org/10.3389/fams.2023.1210404","url":null,"abstract":"Social media addiction (SMA) is the excessive use of social media platforms, resulting in negative consequences for individuals. It is characterized by an uncontrollable urge to use social media, leading to negative effects in human's life. This study aims to construct a mathematical model to conceptualize the transmission dynamics of SMA and explore the underlying mechanisms of this harmful addiction in the framework of fractional derivative. The fundamentals of fractional calculus are listed for examining the model. Equilibrium points are identified, and the reproduction parameter R0 is computed to understand the dynamics of SMA spread. Stability analysis of the equilibria is performed, and the impact of various input parameters is numerically investigated. The existence and uniqueness of the proposed SMA model are demonstrated through simulations, which also study the intricate dynamics with respect to different input factors. To develop effective control strategies, the system's dynamical behavior is examined, and the influence of fractional derivative order on fluctuations is explored. This research offers a range of suggestions aimed at reducing the occurrence of social media addiction.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49493737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-08DOI: 10.3389/fams.2023.1268240
I. Spassiani, M. Taroni, A. Stallone, Pietro Artale Harris
{"title":"Editorial: Physical and statistical approaches to earthquake modeling and forecasting","authors":"I. Spassiani, M. Taroni, A. Stallone, Pietro Artale Harris","doi":"10.3389/fams.2023.1268240","DOIUrl":"https://doi.org/10.3389/fams.2023.1268240","url":null,"abstract":"","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45712227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-03DOI: 10.3389/fams.2023.1206500
M. Cai, H. Gu, P. Hong, Jingzhi Li
Biot's consolidation model in poroelasticity describes the interaction between the fluid and the deformable porous structure. Based on the fixed-stress splitting iterative method proposed by Mikelic et al. (Computat Geosci, 2013), we present a network approach to solve Biot's consolidation model using physics-informed neural networks (PINNs).Two independent and small neural networks are used to solve the displacement and pressure variables separately. Accordingly, separate loss functions are proposed, and the fixed stress splitting iterative algorithm is used to couple these variables. Error analysis is provided to support the capability of the proposed fixed-stress splitting-based PINNs (FS-PINNs).Several numerical experiments are performed to evaluate the effectiveness and accuracy of our approach, including the pure Dirichlet problem, the mixed partial Neumann and partial Dirichlet problem, and the Barry-Mercer's problem. The performance of FS-PINNs is superior to traditional PINNs, demonstrating the effectiveness of our approach.Our study highlights the successful application of PINNs with the fixed-stress splitting iterative method to tackle Biot's model. The ability to use independent neural networks for displacement and pressure offers computational advantages while maintaining accuracy. The proposed approach shows promising potential for solving other similar geoscientific problems.
{"title":"A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's model","authors":"M. Cai, H. Gu, P. Hong, Jingzhi Li","doi":"10.3389/fams.2023.1206500","DOIUrl":"https://doi.org/10.3389/fams.2023.1206500","url":null,"abstract":"Biot's consolidation model in poroelasticity describes the interaction between the fluid and the deformable porous structure. Based on the fixed-stress splitting iterative method proposed by Mikelic et al. (Computat Geosci, 2013), we present a network approach to solve Biot's consolidation model using physics-informed neural networks (PINNs).Two independent and small neural networks are used to solve the displacement and pressure variables separately. Accordingly, separate loss functions are proposed, and the fixed stress splitting iterative algorithm is used to couple these variables. Error analysis is provided to support the capability of the proposed fixed-stress splitting-based PINNs (FS-PINNs).Several numerical experiments are performed to evaluate the effectiveness and accuracy of our approach, including the pure Dirichlet problem, the mixed partial Neumann and partial Dirichlet problem, and the Barry-Mercer's problem. The performance of FS-PINNs is superior to traditional PINNs, demonstrating the effectiveness of our approach.Our study highlights the successful application of PINNs with the fixed-stress splitting iterative method to tackle Biot's model. The ability to use independent neural networks for displacement and pressure offers computational advantages while maintaining accuracy. The proposed approach shows promising potential for solving other similar geoscientific problems.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44638445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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