Abstract
AbstractThe dynamics of particle processes can be described by population balance equations which are governed by phenomena including growth, nucleation, breakage and aggregation. Estimating the kinetics of the aggregation phenomena from measured density data constitutes an ill-conditioned inverse problem. In this work, we focus on the aggregation problem and present an approach to estimate the aggregation kernel in discrete, low rank form from given (measured or simulated) data. The low-rank assumption for the kernel allows the application of fast techniques for the evaluation of the aggregation integral ($\mathcal {O}(n\log n)$
O
(
n
log
n
)
instead of $\mathcal {O}(n^{2})$
O
(
n
2
)
where n denotes the number of unknowns in the discretization) and reduces the dimension of the optimization problem, allowing for efficient and accurate kernel reconstructions. We provide and compare two approaches which we will illustrate in numerical tests.
Funder
DFG
Technische Universität Hamburg
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
Reference16 articles.
1. Bramley, A.S., Hounslow, M.J., Ryall, R.L.: Aggregation during precipitation from solution: A method for extracting rates from experimental data. J. Colloid Interface Sci. 183(1), 155–165 (1996)
2. Brunel, N.J.-B.: Parameter estimation of ODEs via nonparametric estimators. Electronic Journal of Statistics 2(0), 1242–1267 (2008)
3. Buchanan, A., Fitzgibbon, A.: Damped Newton algorithms for matrix factorization with missing data. 2012 IEEE Conference on Computer Vision and Pattern Recognition 2, 316–322 (2005)
4. Catral, M., Han, L., Neumann, M., Plemmons, R.J.: On reduced rank nonnegative matrix factorization for symmetric nonnegative matrices. Linear Algebra and its Applications 393, 107–126 (2004)
5. Chakraborty, J., Kumar, J., Singh, M., Mahoney, A., Ramkrishna, D.: Inverse problems in population balances. Determination of aggregation kernel by weighted residuals. Industrial & Engineering Chemistry Research 54(42), 10530–10538 (2015)
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