Presentation on theme: "Modelling dynamics of electrical responses in plants"— Presentation transcript:
1 Modelling dynamics of electrical responses in plants Sanmitra GhoshSupervisor: Dr Srinandan Dasmahapatra & Dr Koushik MaharatnaElectronics and Software Systems,School of Electronics & Computer ScienceUniversity of Southampton
2 Outline Introduction Black Box models (System Identification) Modelling plant responses as ODEsCalibration of Models (Parameter Estimation in ODE using ABC-SMC)ABC-SMC using Gaussian processesFuture workReferences
11 ABC ABC Rejection Sampler (Pickard, 1999) Given 𝑦, π(θ), 𝑓(x|𝜃) Sample a parameter 𝜃∗ from the prior distribution π(𝜃).Simulate a dataset x from model 𝑓(x| 𝜃∗) with parameter θ∗.if ∆(𝑦, 𝑥) ≤ 𝜀 then5. Accept 𝜃∗ otherwise reject.Note: to generate data x from model 𝑓(x| 𝜃∗) we have to solve the ODE
12 ABC ABC-Sequential Monte Carlo (Toni et al, 1999) 𝜀 1 ≥… ≥ 𝜀 𝑇 𝜀 1 ≥… ≥ 𝜀 𝑇Limitation: extremely slow due to large number of explicit ODE solving for generating simulated data
15 ABC Predator-Pray a b generated 2.10 estimated (ABC-SMC) 2.07 estimated (ABC-SMC-GPDist)2.06Fitzhugh-Nagumoabcgenerated0.203.00estimated (ABC-SMC)0.192.97estimated (ABC-SMC-GPDist)0.210.222.62Mackay-Glassβnγτgenerated2.009.651.00estimated (ABC-SMC)2.079.421.032.01estimated (ABC-SMC-GPDist)2.049.16
16 Future workModel needs to be extended to capture the variability seen among different electrical responses.More models are required to represent other stimuli.
17 References1. J K Pritchard, M T Seielstad, a Perez-Lezaun, and M W Feldman. Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol. Biol. Evol., 16(12):1791–8, December 1999.2. T. Toni, D. Welch, N. Strelkowa, a. Ipsen, and M. P.H Stumpf. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface, 6(31):187–202, February 2009.