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Mathematical Modelling and Simulation

Working Group 8.41

 

 

Machine learning and data driven modelling

Machine learning (ML) refers to the application of algorithms and statistical models to enable computers to recognize patterns in large amounts of data without having to be explicitly programmed to do so.

In medicine, such approaches are used, for example, to optimize diagnostics, to predict the course of diseases or to automatically evaluate medical images such as X-rays and MRI images.

In the field of numerical flow simulation, ML approaches can be used to replace complex computer simulations with simplified (and therefore computationally less expensive) models. This is particularly relevant for determining the uncertainty of measurement processes and optimizing them since this requires a large number of evaluations of the model

Applications

Machine learning for flow profile prediction

Machine learning methods based on artificial neural networks (ANN) are being applied in an increasing number of applications - also in the field of fluid mechanics. Areas to be mentioned are, for instance, turbulence modelling, interpolation of data from coarser to finer resolution, (active) flow control and the prediction of flows also in their temporal development.
In a Opens internal link in current windowTransMeT project in cooperation with working group 3.51 and the company OPTOLUTION, an algorithm based on an ANN is developed that can predict a two-dimensional flow profile of a pipe flow from velocity data along a one-dimensional path. This method will be used, in particular, to reduce the uncertainty of the volumetric flow rate prediction of strongly disturbed velocity profiles - for example due to bends, valves, pipe cross-section changes, etc. - on the basis of path measurements. This method is used in practice for calibration and thus for improving the energy efficiency of drinking water, heating, and cooling networks.

Deep-Learning based determination of boundary layers in multiphase flows

When gas and liquid flow simultaneously through a pipe, different flow patterns can develop. These patterns mainly differ in the distribution of the fluids in the pipe and the associated formation of structures in the flow. Some of these structures negatively affect the measurement accuracy of flow meters. This influence was investigated as part of the EMPIR project "Opens internal link in current windowMultiphase Flow Reference Metrology". This requires detailed characterizations of these flow patterns. For this purpose, a deep-learning model was developed, which extracts the dynamics of the gas-liquid interface in the pipe from high-speed video recordings of the flow, thus enabling classification and characterization. This means that the influence of the flow pattern on the measurement uncertainty can now be further investigated.

Publications

Publication single view

Article

Title: An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum
Author(s): M. Radszuweit, H. Engel;M. Bär
Journal: PloS one
Year: 2014
Volume: 9
Issue: 6
Pages: e99220
Public Library of Science
DOI: 10.1371/journal.pone.0099220
ISSN: 1932-6203
Web URL: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0099220
Keywords: ,Biological,Biomechanical Phenomena,Calcium,Calcium: metabolism,Cytoplasm,Cytoplasm: physiology,Cytoskeleton,Cytoskeleton: physiology,Elasticity,Mechanical,Models,Physarum polycephalum,Physarum polycephalum: cytology,Physarum polycephalum: physiology,Stress,pattern formation
Tags: 8.41, ActMatter, ActFluid
Abstract: Motivated by recent experimental studies, we derive and analyze a two-dimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a description of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The equations for the poroelastic medium are obtained from continuum force balance and include the relevant mechanical fields and an incompressibility condition for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stress. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a mechanochemical coupling. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.

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