Abstract
Bayesian particle filters (PFs) are a viable alternative to sampling methods such as Markov chain Monte Carlo methods to estimate model parameters and related uncertainties when the forward model is a dynamical system, and the data are time series that depend on the state vector. PF techniques are particularly attractive when the dimensionality of the state space is large and the numerical solution of the dynamical system over the time interval corresponding to the data is time consuming. Moreover, information contained in the PF solution can be used to infer on the sensitivity of the unknown parameters to different temporal segments of the data. This, in turn, can guide the design of more efficient and effective data collection procedures. In this article the PF method is applied to the problem of estimating cell membrane permeability to gases from pH measurements on or near the cell membrane. The forward model in this case comprises a spatially distributed system of coupled reaction-diffusion differential equations. The high dimensionality of the state space and the need to account for the micro-environment created by the pH electrode measurement device are additional challenges that are addressed by the solution method.
Original language | English |
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Article number | 094004 |
Journal | Inverse Problems |
Volume | 39 |
Issue number | 9 |
DOIs | |
State | Published - Sep 2023 |
Externally published | Yes |
Funding
This work made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University. The work of D C was supported in part by NSF Award DMS 1951446. The work of E S was supported in part by NSF Award DMS 2204618.
Funders | Funder number |
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National Science Foundation | DMS 2204618, DMS 1951446 |
Keywords
- gas transport
- membrane permeability
- particle filter