Motion of Patterns Modeled by the Gray-Scott Autocatalysis System in One Dimension

Korkmaz, Alper; Ersoy, Özlem; Dağ, İdris

doi:10.48550/arxiv.1605.09712

Cited by 2 publications

(1 citation statement)

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“…Mazin et al [20] replicated and extended previous works and explored the pattern formation from a bifurcation analysis perspective. Korkmaz et al [16] combined the implicit Rosenbrock method with the exponential Bspline configuration method to solve the numerical solution of the 1D autocatalytic system. Manaa et al [19] numerically solved the 1D model using successive approximation and finite difference methods.…”

Section: Related Workmentioning

confidence: 99%

Physics-informed neural networks approach for 1D and 2D Gray-Scott systems

Giampaolo

Rosa

et al. 2022

Adv. Model. and Simul. in Eng. Sci.

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Nowadays, in the Scientific Machine Learning (SML) research field, the traditional machine learning (ML) tools and scientific computing approaches are fruitfully intersected for solving problems modelled by Partial Differential Equations (PDEs) in science and engineering applications. Challenging SML methodologies are the new computational paradigms named Physics-Informed Neural Networks (PINNs). PINN has revolutionized the classical adoption of ML in scientific computing, representing a novel class of promising algorithms where the learning process is constrained to satisfy known physical laws described by differential equations. In this paper, we propose a PINN-based computational study to deal with a non-linear partial differential equations system. In particular, using this approach, we solve the Gray-Scott model, a reaction–diffusion system that involves an irreversible chemical reaction between two reactants. In the unstable region of the model, we consider some a priori information related to dynamical behaviors, i. e. a supervised approach that relies on a finite difference method (FDM). Finally, simulation results show that PINNs can successfully provide an approximated Grey-Scott system solution, reproducing the characteristic Turing patterns for different parameter configurations.

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Section: Related Workmentioning

confidence: 99%