Revisiting Fisher-KPP model to interpret the spatial spreading of invasive cell population in biology

Paul, Gour Chandra; Tauhida, None; Kumar, Dipankar

doi:10.1016/j.heliyon.2022.e10773

Cited by 6 publications

(2 citation statements)

References 36 publications

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“…In prior research, hybrid modeling has proven effective in addressing issues related to parametric uncertainties within simpler model equations. , However, applying this approach to complex systems described by PDEs presents its own distinct challenges. In this study, we narrow our focus to a particular category of systems known as reaction–diffusion, frequently expressed as Fisher-KPP models , or Porous Fisher models. , Reaction–diffusion processes play a fundamental role in various scientific fields including biology, chemistry, and physics. These processes describe the spatiotemporal dynamics of substances undergoing both diffusion (the spreading of substances through space) and chemical reactions.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, we narrow our focus to a particular category of systems known as reaction−diffusion, frequently expressed as Fisher-KPP models 38,39 or Porous Fisher models. 40,41 Reaction−diffusion processes play a fundamental role in various scientific fields including biology, chemistry, and physics. These processes describe the spatiotemporal dynamics of substances undergoing both diffusion (the spreading of substances through space) and chemical reactions.…”

Section: Introductionmentioning

confidence: 99%

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Unveiling Latent Chemical Mechanisms: Hybrid Modeling for Estimating Spatiotemporally Varying Parameters in Moving Boundary Problems

Pahari,

Shah,

Sang-Il Kwon

2024

Ind. Eng. Chem. Res.

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Hybrid modeling has gained substantial recognition due to its capacity to seamlessly integrate machine learning methodologies while preserving the fundamental physical principles inherent in a model. Although these hybrid models have predominantly been applied to temporal processes governed by ordinary differential equations, the intricacies of various real-world systems, characterized by a diverse array of physical processes, extend far beyond this domain. This study extensively investigates the application of hybrid modeling techniques within the context of a complex biological system regulated by the reaction−diffusion equation, a specific type of partial differential equation. The primary objective is to tackle the challenges associated with latent chemical mechanisms that are concealed from direct observation. The proposed approach introduces a hybrid modeling framework that synergizes neural networks with mathematical methods to estimate parameters exhibiting spatiotemporal variations within a category of problems involving dynamic boundaries. Model training is executed through a back-propagation algorithm, adept at efficiently updating these parameters while ensuring numerical stability. Subsequently, the hybrid model is employed in the context of reaction−diffusion models, yielding results that validate its proficiency in precisely estimating variable diffusivity across both space and time as well as temporal fluctuations in cell proliferation rates and cell carrying density. The mean squared error of the final output predictions by the hybrid model is 9.4 × 10 −6 as compared to that of a simple first-principles model which is 3.12 × 10 −4 .

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