ECSW Hyperreduction Code and Tests

[biondicc]

Pull request for the addition of the energy-conserving sampling and weighting hyperreduction technique into the projection-based ROMs previously tested.

Non-negative least squares solver (added to the linear_solver directory):

• Implemented the NNLS algorithm developed by Lawson and Hanson (presented in Solving Least Squares Problems https://epubs.siam.org/doi/10.1137/1.9781611971217 )
• The NNLS solver can be modified via the inputs to the class:
• By default the internal loop least squares problem is solved directly using the Normal equations, by setting itersolver to true an iterative solver can be used instead
• By default the exit criterion is the update to the original Lawson algorithm presented by Chapman et al. in Accelerated mesh sampling for the hyper reduction of nonlinear computational models https://doi.org/10.1002/nme.5332. This can be changed back to the original gradient based exit condition presented by Lawson.
• A helper file was added which contains multiple functions for changing between Epetra and Eigen data structures.

ode_solver directory changes:

• Added hyperreduced PG solver, following the structure of the other ROM solvers with new functions to find the hyperreduced residual and Jacobian

parameters directory changes:

• Renamed one of the POD tests from old ROM code (POD_adaptive_sampling -> POD_adaptive_sampling_run)
• Added parameters_hyper_reduction.cpp to control hyperreduction and NNLS solver settings

reduced_order directory changes:

• Moved pod_adaptive_sampling.cpp/h from the tests folder and made it into a class
• Created a base class for which adaptive sampling with and without hyperreduction are built on top of
• Added code to assemble the training data for the NNLS problem, using a base class and two derived classes for the residual and Jacobian-based ECSW approaches
• A third sampling procedure class (hyper_reduced_sampling_error_updated.cpp) is implemented with the new DWR error indicator which depends on the new test location class (hrom_test_location.cpp)

Test changes:

• pod_adaptive_sampling.cpp was moved into a class, and the pod_adaptive_sampling_run.cpp test can be used to build an instance of this class and run the sampling procedure to the tolerance set in the parameter file
• hyper_adaptive_sampling_run.cpp and hyper_adaptive_sampling_new_error.cpp perform similar tests running the sampling procedure with hyperreduction in both and the updated DWR error in the latter
• hyper_reduction_post_sampling.cpp will conduct hyperreduction after the sampling procedure has been completed, and hyper_reduction_comparison.cpp will do the same and compare it to a similar ROM without hyperreduction
• build_NNLS_problem.cpp will test the assembly and results of a sample NNLS problem built from a ROM problem
• ROM_error_post_sampling.cpp and HROM_error_post_sampling will find the "true" error at 400 evenly distributed points for the NACA 0012 transonic 2 parameter test case for a ROM without and with hyperreduction, respectively

[cpethrick]

Everything looks good on my end!

Great work on this PR, you've done a lot of good work with reorganizing the ROM portion of the code! I hope that your changes make it easier for future students to continue development of ROM/HROM :)

I will approve once you post the ctest results.

[sonarcloud[bot]]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
No data about Coverage
No data about Duplication

See analysis details on SonarCloud

[biondicc]

Here are the files which contain the tests that fail when I run ctest in my branch.

The first (Failed.log) is before I updated the helper functions, which were causing some of the hyperreduction tests to fail. Failed.log

Once I updated the helper functions/some of the tolerances in my prm files in the latest commit, I re-ran ctest from test 274 onwards and the hyperreduction tests all passed, this was the new failed test log. LastTestsFailed.log

Thank you to the reviewers for all your helpful comments and support! Let me know if there are still open questions.