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294: [WIP] Resolving some test problem consistency and apparent UKI instability r=odunbar a=odunbar <!--- THESE LINES ARE COMMENTED --> ## Purpose <!--- One sentence to describe the purpose of this PR, refer to any linked issues: #14 -- this will link to issue 14 Closes #2 -- this will automatically close issue 2 on PR merge --> Closes #287 ## Content <!--- specific tasks that are currently complete - Solution implemented --> - more consistent plotting between tests - adjustments to the test problems - removed inappropriate Localization tests in `EnsembleKalmanProcess/runtests.jl` examples, (they are already properly tested in `Localizers/runtests.jl` ) - These caused blow up without disturbing the ensemble mean, therefore added some spread-checking too to ensure the tr(ensemble cov) does not increase too much - test UKI with nonlinear problems, not just linear ones - Added prior Tikhonov regularization for UKI, modified test checks to account for the regularization. - Changed the default `update_freq` in UKI from 1 to 0. I.e. uses prior cov not current cov by default. - Minor type change in UKI constructor to allow arrays to be converted to float type internally - added note to docs RE this update <!--- Review checklist I have: - followed the codebase contribution guide: https://clima.github.io/ClimateMachine.jl/latest/Contributing/ - followed the style guide: https://clima.github.io/ClimateMachine.jl/latest/DevDocs/CodeStyle/ - followed the documentation policy: https://github.com/CliMA/policies/wiki/Documentation-Policy - checked that this PR does not duplicate an open PR. In the Content, I have included - relevant unit tests, and integration tests, - appropriate docstrings on all functions, structs, and modules, and included relevant documentation. --> ---- - [ ] I have read and checked the items on the review checklist. ## UPDATED Example: To reproduce run `julia --project; ENV["CES_TEST_PLOT_OUTPUT"] = true; ]; test` and look for the figures `XYZ_test_4.png` in the runtest directory. Problem: `x in R^2`, and `y = (||x-x*||_1,||x-x*||_2, ||x-x*||_infty ) + N(0,0.01)`, 100 iterations of methods: Prior bounded by `[-2,2]` in x axis ### EKI & EKS <img src="https://github.com/CliMA/EnsembleKalmanProcesses.jl/assets/47412152/ac03092e-b0b6-4fb6-8dd0-8ab000f5c2a8" width=300> <img src="https://github.com/CliMA/EnsembleKalmanProcesses.jl/assets/47412152/7a275262-a1ee-4bc8-a7cb-b71743387c96" width=300> ### Tikhonov UKI quad & simplex <img src="https://github.com/CliMA/EnsembleKalmanProcesses.jl/assets/47412152/38017e26-45ac-4b5e-9dc3-15dbd548d040" width=300> <img src="https://github.com/CliMA/EnsembleKalmanProcesses.jl/assets/47412152/21748770-4aa4-47ba-b62f-c70aa57c03bc" width=300> Co-authored-by: odunbar <[email protected]>
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