LEMDA: Lagrangian-Eulerian Multiscale Data Assimilation
This MATLAB package documents the algorithms for the LEMDA framework. In particular, it generates the Figures in the submitted LDEMA paper. Several comments are
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For Figures 2, 3, and 4, run LaDA_floe.m in folder LaEuDA. There are several loops for different beta values (drag coefficients) and L (number of particles) values. We can modify the beta values in line 16 and L values in line 9 in this file LaDA_floe.m as well as the corresponding beta and L values in line 2 in search_r_equil.m to generate the individual cases and combine them to generate these Figures 2, 3, and 4.
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For Figure 5 and panels (a)-(c) of Figure 6, run EuDAloop2.m in folder LaEuDA to generate all the synthetic data and EuDA posterior means and covariances for L=j*500, j=1,2,...16, number of floes. This will produce panel (c) of Figure 6. Then uncomment lines 202 to 373 in EuDAloop2.m to generate the panels (a)-(c) of Figure 5. For panel (d) of Figure 5, run rmsepccPhyDomainEuDA.m and then ``Run Section" (Matlab functionality) of the section of lines 43 to 67. Similar to panel (d) of Figure 5, run the saved data to generate panels (a)-(b) of Figure 6. For panel (d) of Figure 6, it is similar to the loop on the number of particles. Herein, the loop is on the grid size. Run EuDAloop3nx.m in folder LaEuDA.
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For Figures 7, 8 and 9, the simulation settings are very similar to those of Figures 5 and 6, except that herein particle collisions are included, leading to a much higher demand on computational hours. To generate Figure 7, run LaDAloopSigv.m in folder LaEuDA. Therein, to produce panels (a)-(d), set setsigv = 0.0 in line 63 in LaDAloopSigv.m. To produce panel (e), use the default setsigv = (1:11)*0.02-0.02 in line 63 in LaDAloopSigv.m. set To generate Figures 8 and 9, run EuDAloop2CF.m and EuDAloop3nxCF.m in folder LaEuDA. The simulations for Figures 8 and 9 in the paper were done in the Australian National Computing Infrastructure (NCI) national facility under project zv32 in a parallel environment. There were commented lines in EuDAloop2CF.m and EuDAloop3nxCF.m for the parallel computation setting which can be easily adjusted in a different parallel environment. As these loop files require substantial computational costs, we suggest adjusting these codes accordingly to run parallel computing.
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For Figure 10, run LEMDA.m in the LEMDA folder to generate a set of Figures then use them as subfigures for Figure 9. Similar to the process for Figures 8 and 9, the simulations for these figures take a significant amount of time to run. We recommend adjusting the codes to enable parallel computing for improved efficiency, particularly for the local LaDA part in each cell of the 7x7 grid.
LEMDA: Lagrangian Eulerian Multiscale Data Assimilation
If you intend to use this package, please acknowledge the authors and the source, particularly by citing our work on LEMDA.
Permission to use this work is granted, provided that the copies are not made or distributed for commercial purposes and provided that NO WARRANTY, express or implied, of merchantability or fitness for any particular purpose is made with respect to products which have been altered, subjected to abuse or improperly used. Under no circumstances will the author be liable for any damages, lost profits, malpractice claims, inconvenience, or any other losses caused by the use of this package.
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(c) Quanling Deng, 2022-2024 [email protected]; [email protected]
School of Computing Australian National University