Forecasting research trends using population dynamics model with Burgers' type interaction

Jabłońska, Matylda; Sitarz, Robert; Krasławski, Andrzej

doi:10.1016/b978-0-444-63234-0.50104-4

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…Regarding document analysis, in process engineering, the first studies began to appear with the aim of predicting research trends (Jabłońska-Sabuka et al, 2014) or or to studying knowledge flow in research topics . However, documents can be used not only to simulate creativity as previously mentioned but also to create a community for problem resolution and idea generation (Section 3).…”

Section: Cai In Chemical Process Engineeringmentioning

confidence: 99%

Open computer aided innovation to promote innovation in process engineering

Flores

Belaud

Negny

et al. 2015

Chemical Engineering Research and Design

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Section: Cai In Chemical Process Engineeringmentioning

confidence: 99%

Open computer aided innovation to promote innovation in process engineering

Flores

Belaud

Negny

et al. 2015

Chemical Engineering Research and Design

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“…Solving the Burger's equation allows to determine the ŕuid velocity őeld at a given time and spatial location. This equation has several applications in biology like modeling blood ŕow in the cardiovascular system [45], modeling pattern formation biological systems and modeling population dynamics [46]. Two types of Burgers equations are considered, those without viscosity term which can be obtained by considering the particles non-interaction and whose solution can be realized with the help of the őnite method, including the derivatives approximation means of Taylor developments based on the discretization of the phase space with viscosity term.…”

Section: Burger's Equationmentioning

confidence: 99%

Unsupervised physics-informed neural network in reaction-diffusion biology models (Ulcerative colitis and Crohn’s disease cases) A preliminary study

Rebai,

Boukhris,

Toujani

et al. 2023

Preprint

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We propose to explore the potential of physics-informed neural networks (PINNs) in solving a class of partial differential equations (PDEs) used to model the propagation of chronic inflammatory bowel diseases, such as Crohn’s disease and ulcerative colitis. An unsupervised approach was privileged during the deep neural network training. Given the complexity of the underlying biological system, characterized by intricate feedback loops and limited availability of high-quality data, the aim of this study is to explore the potential of PINNs in solving PDEs. In addition to providing this exploratory assessment, we also aim to emphasize the principles of reproducibility and transparency in our approach, with a specific focus on ensuring the robustness and generalizability through the use of artificial intelligence. We will quantify the relevance of the PINN method with several linear and non-linear PDEs in relation to biology. However, it is important to note that the final solution is dependent on the initial conditions, chosen boundary conditions, and neural network architectures.

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Forecasting research trends using population dynamics model with Burgers' type interaction

Cited by 2 publications

References 18 publications

Open computer aided innovation to promote innovation in process engineering

Open computer aided innovation to promote innovation in process engineering

Unsupervised physics-informed neural network in reaction-diffusion biology models (Ulcerative colitis and Crohn’s disease cases) A preliminary study

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