Add GaussianRandomFields to ParameterDistributions #252
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Function-space representation of input and output space
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Zhengyu-Huang
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Mar 23, 2023
Project.toml format add plot to tests fix global_rng consistency improved interface and seperated coeff vs function sampling constrained sampling from distribution and testing sample from prior test changed transforms to be more consistent and compatible with func dists removed dimensional ambiguities in ndims for functions and tested c->u and u->c get_logpdf -> logpdf 2D examples, unit tests done docstrings codecov docstrings format docstring? docstrings Darcy example removed additional sampling in KL adjusted tests for user dist, and new func construction removed unnecessary functions plot bugfix fixed bug runtest removed rng from build without coeffs, more robust tests rm rng codecov re-open all tests
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Purpose
This PR will enable users to learn parameters that are discretizations of functions.
Content
GaussianRandomField <: FunctionParameterDistributionType <: ParameterDistributionTypeGaussianRandomFields.jlas the back-endParameterDistribution, the user provides a single constraint and this constraint is applied to all discretization points when the function is constructed and constrained.xin unconstrained space.u->cwill transform the unconstrained to constrained coefficients, then builds the unconstrained function, then constrains this functionexample/DarcyNote: 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)constraintThe unconstrained 2D sample
Results from Darcy Flow:
Prior Mean
Final Ensemble Mean
Truth