Odkrivanje kontinuumskih dinamičnih enačb iz delčnih simulacij na primeru preproste tekočine

Jug, Matevž (author), Svenšek, Daniel (mentor), Potisk, Tilen (co-mentor)

V delu predstavimo regresijsko metodo za odkrivanje kontinuumskih dinamičnih enačb iz simulacij, osnovano na algoritmu SINDy. Njeno uporabnost pri odkrivanju makroskopskih enačb preučimo na primeru delčne simulacije preproste tekočine. Pri identificiranih dinamičnih enačbah komentiramo smiselnost posameznih členov in analiziramo natančnost koeficientov pred njimi. Predstavimo in preizkusimo tudi nekaj kriterijev, ki bi lahko pomagali pri izbiri najustreznejšega modela med vsemi identificiranimi.

• Language: Slovenian
• Keywords: redka regresija, SINDy, simulacije, disipativna delčna dinamika, Navier-Stokesova enačba
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-152114-1f15d2c2-414e-83b0-e744-88adf94014ac
• COBISS.SI-ID: 171180803
• Publication date in RUL: 05.11.2023

Secondary language

• Language: English
• Title: Discovering continuum dynamical equations from particle-based simulations: a simple fluid example

Abstract

We present a regression method based on the SINDy algorithm that can be used to discover continuum dynamical equations from simulations. Its usefulness for the discovery of macroscopic equations is investigated on a particle-based simulation of a simple fluid. When examining identified equations, we comment on the meaningfulness of individual terms and analyze the accuracy of their coefficients. We also present and test selected criteria for choosing the most suitable model among the identified.

• Keywords: sparse regression, SINDy, simulations, dissipative particle dynamics, Navier-Stokes equation