Gaussian Random Field parameters #251
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odunbar
added this to the Function-space representation of input and output space milestone
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Apr 19, 2023
252: Add GaussianRandomFields to ParameterDistributions r=odunbar a=odunbar <!--- THESE LINES ARE COMMENTED --> ## Purpose - Addresses #251 This PR will enable users to learn parameters that are discretizations of functions. <!--- 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 --> ## Content <!--- specific tasks that are currently complete - Solution implemented --> - Currently allows: ND -> 1D functions with zero-mean allowed, stored flat. - hierarchy: `GaussianRandomField <: FunctionParameterDistributionType <: ParameterDistributionType` - We use the package `GaussianRandomFields.jl` as the back-end - We provide a default for the prior coefficients distribution under-the-hood, when given a GRF. Otherwise we allow a user-defined coefficient parameter distribution - When built as a `ParameterDistribution`, the user provides a single constraint and this constraint is applied to all discretization points when the function is constructed and constrained. - Compatible with the transform mappings: for parameter distributions. E.g the default is now, given coefficients vector `x` in unconstrained space. `u->c ` will transform the unconstrained to constrained coefficients, then builds the unconstrained function, then constrains this function - Docstrings - Darcy Flow Example in `example/Darcy` Note: We generate truth and solve problem with efunction expansion. ### Plots from Tests 1D Samples of the default prior distribution based on `GRF(Matern(smooth. 1.0,corr. len. 0.1))`  A 2D sample with `bounded(-5,-3)` constraint  The unconstrained 2D sample  ### Results from Darcy Flow: **Prior Mean**  **Final Ensemble Mean**  **Truth**  <!--- 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. --> ---- - [x] I have read and checked the items on the review checklist. Co-authored-by: odunbar <[email protected]>
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This will enable parameters to be based in a function space, As a first stage we could look at representations using Gaussian Random Fields, using the package
GaussianRandomFields.jlThe text was updated successfully, but these errors were encountered: