Model input and output dimension reduction using Karhunen Loève expansions with application to biotransport
Links to Fileshttps://arxiv.org/abs/1903.06314
MetadataShow full item record
Type of Work10 pages
journal articles preprints
Citation of Original PublicationAlen Alexanderian, William Reese, Ralph C. Smith, Meilin Yu, Model input and output dimension reduction using Karhunen Loève expansions with application to biotransport, Physics , Computational Physics, 2019, https://arxiv.org/abs/1903.06314
RightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
We consider biotransport in tumors with uncertain heterogeneous material properties. Specifically, we focus on the elliptic partial differential equation (PDE) modeling the pressure field inside the tumor. The permeability field is modeled as a log-Gaussian random field with a prespecified covariance function. We numerically explore dimension reduction of the input parameter and model output. Truncated Karhunen–Lo`eve (KL) expansions are used to decompose the log-permeability field, as well as the resulting random pressure field. We find that although very high-dimensional representations are needed to accurately represent the permeability field, especially in presence of small correlation lengths, the pressure field is not very sensitive to high-order KL terms of the input parameter. Moreover, we find that the pressure field itself can be represented accurately using a KL expansion with a small number of terms. These observations are used to guide a reduced-order modeling approach to accelerate computational studies of biotransport in tumors.