Extended Parmest Capability for weighted SSE objective

[slilonfe5]

Fixes # .

Summary/Motivation:

Currently, the Parmest SSE objective does not support measurements in different units. This work adds new capabilities to Parmest, including weighted SSE to handle measurements in different units, and more robust covariance matrix calculation methods for more accurate uncertainty quantification. This work also enables the calculation of the covariance matrix using a user-supplied measurement error standard deviation.

Changes proposed in this PR:

• Added a weighted SSE objective
• Added two covariance matrix calculation methods for both the SSE and weighted SSE objectives
• Enabled calculation of the covariance matrix using a user-supplied measurement error standard deviation
• Added a separate function for the covariance matrix estimation

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[slilonfe5]

@adowling2 @djlaky

[adowling2]

@slilonfe5 Here is some quick feedback

compute_jacobian function

• Make this a private method by adding _ to the function name
• Add as an argument to the function relative_perturbation
• In the document string, explain this is using forward (?) finite difference
• Add as an argument the solver object. You can make the default Ipopt.

Feedback on the compute_FIM method:

• Add relative_tolerance and solver as arguments
• Also add a check that error_list must be the same length as y_hat_list
• Add a debugging step for the linear algebra error, compute the condition number of the Jacobian matrix and print it out
• Why would you ever get a linear algebra error for just matrix multiplication? Is this check even needed?

[slilonfe5]

@adowling2 @djlaky I also updated the calculation for the normal SSE such that we can use the user-supplied measurement error if defined; otherwise, we calculate the measurement error as usual.

[adowling2]

Nice progress. I think it is time to start writing tests for the new capabilities.

[adowling2]

@slilonfe5 Once you have the tests ready, tag us for feedback. Also, I think you can skip adding this to the depreciated class.

[adowling2]

Here is more feedback as you work on getting this ready for the Pyomo team to review.

[slilonfe5]

@adowling2 @djlaky I have created a separate method (cov_est) for computing the covariance matrix, supporting three calculation methods (jacobian, kaug, and reduced_hessian). I implemented these covariance calculation methods for both the SSE and SSE_weighted objectives. Lastly, as you suggested, I did not add the new capability to the deprecated interface.

I tested these with three examples (2 steady state and 1 dynamic), and all work well. I'm yet to write the test file for these.

[slilonfe5]

@blnicho @mrmundt @jsiirola @adowling2 @djlaky I have implemented Miranda's final review on this PR. I think this can be moved to Reviewer Approved in the August 2025 Release dashboard.

[slilonfe5]

@mrmundt @blnicho Just a kind reminder that this PR is waiting for Reviewer Approval. Thanks

[slilonfe5]

@blnicho Just a kind reminder that I'm waiting for your pending comments (the ones you mentioned during Tuesday's meeting). Thanks

[blnicho]

@slilonfe5 here are some initial comments/suggestions. I'm still going through a couple of the files but I have some more substantial questions that I'll message you separately about.

[blnicho]

@slilonfe5 here are a few more review comments. I'm still going through parmest.py

[blnicho]

I think you only end up in this else-statement when cov_method="reduced_hessian". Why don't these covariance values match the expected values from the paper or the values calculated using the other methods?

[slilonfe5]

We are using the true sse to compute the covariance matrix. Previously, we calculated the covariance by assuming that the obj_val is the sse, which is not true.

[blnicho]

So the three calculation methods aren't approximating the same sse and covariance?