Seminarium z fizyki biologicznej i bioinformatyki
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2024-03-06 (15:15) 
Jan Wróblewski (Institute of Informatics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw)
Quantitative comparison of reaction-diffusion cellular automata with partial differential equations
https://zoom.us/j/91976153012?pwd=azNiMWE4UnhPN3lRQlY2UHZHOXVkQT09
Meeting ID: 919 7615 3012
Passcode: 747922
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Bogdan Lesyng (UW)
Anna Niedźwiecka (IF PAN)
Piotr Zielenkiewicz (IBB)
Abstract
Cellular automata (CA) are used to simulate physical processes with various degrees of precision, but vast majority of CA has not been theoretically proven to converge to their well-established PDE model counterparts. We present a stochastic reaction-diffusion CA with a parameter that can increase its precision by increasing the number of molecules within. We show how its solutions converge to the PDE model as parameters improve. These theoretical results give confidence in the accuracy of the CA model itself, but the error bounds are small enough only for impractically computationally intensive precision parameters. Therefore, we experimentally show that, even for small precision parameters, we obtain good quantitative and qualitative similarity between CA and PDE simulations. We discuss the methods and challenges of quantitatively comparing these models as well as discuss a few interesting findings about the specific reaction-diffusion modeled by them.
Meeting ID: 919 7615 3012
Passcode: 747922
One tap mobile
+48223073488,,91976153012#,,,,*747922# Poland
+48223987356,,91976153012#,,,,*747922# Poland
Dial by your location
+48 22 307 3488 Poland
+48 22 398 7356 Poland
+48 22 306 5342 Poland
Bogdan Lesyng (UW)
Anna Niedźwiecka (IF PAN)
Piotr Zielenkiewicz (IBB)
Abstract
Cellular automata (CA) are used to simulate physical processes with various degrees of precision, but vast majority of CA has not been theoretically proven to converge to their well-established PDE model counterparts. We present a stochastic reaction-diffusion CA with a parameter that can increase its precision by increasing the number of molecules within. We show how its solutions converge to the PDE model as parameters improve. These theoretical results give confidence in the accuracy of the CA model itself, but the error bounds are small enough only for impractically computationally intensive precision parameters. Therefore, we experimentally show that, even for small precision parameters, we obtain good quantitative and qualitative similarity between CA and PDE simulations. We discuss the methods and challenges of quantitatively comparing these models as well as discuss a few interesting findings about the specific reaction-diffusion modeled by them.