Goal-Oriented Adaptive Sampling and Addition of Eigen Library

[donovan97]

Pull request for goal-oriented adaptive sampling for reduced-order models and the addition of the Eigen library to the code.

The pull request introduces significant changes to the reduced-order modeling. All of the old reduced-order modeling code is replaced as it did not work for cases run on multiple processors. Unused code and tests were also removed.

Summary of main changes:

Changes to Functional class:

• The partial second derivatives of the class that are dealii::TrilinosWrappers::SparseMatrix are changed to pointers. This is because the dealii::TrilinosWrappers::SparseMatrix class has a virtual destructor to use pointers to the class, see https://www.dealii.org/current/doxygen/deal.II/classTrilinosWrappers_1_1SparseMatrix.html#adbe89a97bc7ef4bbc16e5e04b72bb19e As a result of the virtual destructor, I was encountering errors due to the dealii::TrilinosWrappers::SparseMatrix within the Functional class when the Functional object in the functionalFactory method (pod_adaptive_sampling.cpp) went out of scope. The solution was to make the SparseMatrices pointers, and use a pointer to the Functional base class for the functionalFactory function in pod_adaptive_sampling.cpp. The destructor for the Functional class is also made virtual as this is supposed to be the case for a base class. Update July 11: The functionalFactory method in pod_adaptive_sampling.cpp was removed and instead the FunctionalFactory class in functional.cpp is being used.

ODE solver changes:

• Galerkin and Petrov-Galerkin ODE solvers have been updated to work in parallel and to ensure solution consistency (reduced-order solution at snapshot point is exactly the full-order solution).

Test changes:

• reduced_order.cpp now tests for consistency of the reduced-order model. Tested on Burgers Rewienski and NACA0012 FlowSolver cases.
• pod_adaptive_sampling.cpp performs an adaptive snapshot sampling for the reduced-order model. Tested on Burgers Rewienski and NACA0012.
• adaptive_sampling_testing.cpp is used for validation testing and producing additional results, it does not actually test anything. Tests using this will be commented out before merging.

reduced_order directory changes:

• Removal of all files previously in this directory.
• pod_interface.h provides an interface for the types of POD (offline and online POD)
• pod_basis_offline.cpp computes a POD basis from previously computed snapshots
• pod_basis_online.cpp computes a POD basis "online", during the adaptive sampling process
• min_max_scaler.cpp scales data between 0 and 1, used before interpolating
• rbf_interpolation.cpp implements a radial basis function interpolation
• nearest_neighbors.cpp implements k nearest neighbors for use with adaptive sampling
• reduced_order_solution.cpp stores information about a reduced order solution that is required in future iterations of adaptive sampling
• rom_test_location.cpp computes adjoint-based error estimates for adaptive sampling
• halton.cpp computes a Halton sequence. I did not write this file, no need to review it.

Addition of Eigen library:

The pull request also adds the Eigen library as a submodule (see .gitmodules). Therefore, after merging the PR, everyone will have to update their git submodules to download the Eigen library in the submodules directory. This may need to be done with the command: git submodule update --init --recursive

All required tests are passing and the addition of Eigen is not causing issues on Narval.

[jbrillon]

I added @cpethrick since she's working with the ODE solver

[donovan97]

Great PR. The addition of the Eigen library seems very convenient, and it looks like you've put significant effort towards improving the reduced-order capabilities of PHiLIP. There's already been some great discussion already about the ODE Solver section, which I contributed to where I saw fit. I have a few fairly minor comments.

Does the addition of the Eigen library necessitate an update to the documentation/readme/installation files? If so, that should be added to your PR.

Since Eigen was added as a submodule, git should handle it automatically for a new installation, like the other existing submodules. For anyone who already has PHiLiP installed, you will likely need to update your git submodules using the command: git submodule update --init --recursive

[dougshidong]

Thanks everyone for the thorough review and great job. There was a relatively high number of changes and the review comments were all insightful. Thanks for making the changes as well Donovan.

Keep it up.