Berlin 2012 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 7: Reaction-Diffusion-Systems

DY 7.4: Vortrag

Montag, 26. März 2012, 17:30–17:45, MA 144

Parameter estimation for reaction-diffusion systems — •Andreas Ruttor and Manfred Opper — Technische Universität Berlin

Spatial fluctuations of the particle density in reaction-diffusion systems are often modelled by dividing the system into small compartments. In this case, additional transfer reactions describe the diffusion, so that methods for homogeneous reactions systems can be used in order to estimate parameters. However, finding a suitable discretization is not easy: if the compartments are too big, important spatial structure contained in the observations is lost. But using smaller compartments increases the complexity of the calculations. In order to solve this problem, we propose a more fundamental approach. Instead of using compartments directly, we transform the model into Fourier space and calculate the continuum limit analytically. As before, the dynamics of the system is described by its Fokker-Planck equation. We then apply system size and weak noise expansions, which lead to a Gaussian approximation suitable for efficient parameter estimation. It turns out that only low-frequency moments are relevant here, while higher frequencies mostly contain noise. This also applies to the observations, as it is impossible to measure all details of the spatial fluctuations. Consequently, only a small number of moments in Fourier space are needed for calculating the total likelihood, usually less than in the case of compartment models.