Add Enzyme vs DependencyTracking system Jacobian test and benchmark over all PhasorDynamics cases

[nkoukpaizan]

Description

This adds an integration test for full-system Enzyme vs DependencyTracking Jacobians. The test loops over all files in cases/PhasorDynamics/ to compute and compare Jacobians via Enzyme and DependencyTracking. A benchmarking phase times the setup, residual evaluation and Jacobian assembly costs.

On my macOS, ctest --verbose -R PhasorDynamicsIntegrationSystemJacobian generates:

71: [SUMMARY] Times in us per call (setup once); ratio = DependencyTracking / Enzyme.
71: case                    method                 size     nnz      setup   ratio  residual   ratio  Jacobian   ratio
71: ThreeBusZipLoad         Enzyme                   16      60        9.3               0.1               0.4
71: ThreeBusZipLoad         DependencyTracking       16      60       29.6     3.2       7.5    97.0       1.2     3.2
71: ThreeBusClassical       Enzyme                   16      60        9.8               0.1               0.4
71: ThreeBusClassical       DependencyTracking       16      60       27.7     2.8       7.0    93.8       1.2     3.3
71: TwoBusBasic             Enzyme                   19      68       10.1               0.0               0.3
71: TwoBusBasic             DependencyTracking       19      68       33.5     3.3       7.1   246.3       1.4     4.2
71: TwoBusTgov1             Enzyme                   22      76        7.8               0.0               0.4
71: TwoBusTgov1             DependencyTracking       22      76       32.8     4.2       9.2   241.5       1.5     3.7
71: ThreeBusConstantSource  Enzyme                   23      88        8.7               0.1               0.5
71: ThreeBusConstantSource  DependencyTracking       23      88       29.1     3.3      10.0   151.0       1.8     3.6
71: TwoBusIeeet1            Enzyme                   31     100       10.1               0.1               0.6
71: TwoBusIeeet1            DependencyTracking       31     100       33.6     3.3      12.3   237.4       2.0     3.7
71: TwoBusGensal            Enzyme                   32     107       18.4               0.1               0.5
71: TwoBusGensal            DependencyTracking       32     107       63.1     3.4      13.0   173.3       2.2     4.1
71: ThreeBusBasic           Enzyme                   40     152       11.8               0.1               0.8
71: ThreeBusBasic           DependencyTracking       40     152       45.5     3.9      16.3   203.6       3.1     3.9
71: TwoArea                 Enzyme                  140     512       77.4               0.4               3.1
71: TwoArea                 DependencyTracking      140     512      198.0     2.6      66.8   164.2      10.6     3.4
71: IEEE39                  Enzyme                  518    2014      136.8               1.4              10.9
71: IEEE39                  DependencyTracking      518    2014      489.0     3.6     249.1   181.0      43.1     4.0
71: Hawaii                  Enzyme                 1652    5721      381.3               6.1              34.2
71: Hawaii                  DependencyTracking     1652    5721     1720.0     4.5    1111.1   181.1     125.9     3.7
71: ACTIVSg200              Enzyme                 1538    6880      518.1               9.1              39.9
71: ACTIVSg200              DependencyTracking     1538    6880     1656.3     3.2    1005.9   110.4     150.9     3.8
71: ACTIVSg500              Enzyme                 2804   13244      992.2              20.7              79.4
71: ACTIVSg500              DependencyTracking     2804   13244     3084.9     3.1    2192.7   106.1     297.6     3.7
71: WECC240                 Enzyme                 5668   20732     1611.2              27.0             123.6
71: WECC240                 DependencyTracking     5668   20732     6918.4     4.3    4728.5   175.2     452.2     3.7
71: ACTIVSg2000             Enzyme                20312   84627     7335.2             125.6             561.4
71: ACTIVSg2000             DependencyTracking    20312   84627    22021.7     3.0   16900.8   134.5    1972.1     3.5
71: ACTIVSg10k              Enzyme                92834  379712    48768.5            1315.2            5852.6
71: ACTIVSg10k              DependencyTracking    92834  379712   119509.7     2.5   67507.6    51.3    8263.9     1.4

The largest cost differences occur in evaluateResiduals, where DependencyTracking has the overhead of tracking. The std::map manipulations for Jacobian assembly are not as bad as I thought.

Checklist

• All tests pass.
• Code compiles cleanly with flags -Wall -Wpedantic -Wconversion -Wextra.
• The new code follows GridKit™ style guidelines.
• There are unit tests for the new code.
• The new code is documented.
• The feature branch is rebased with respect to the target branch.
• The CHANGELOG.md has been updated to reflect the changes. If this is a minor PR that is part of a larger fix already included in the file, state so.

Further comments

The change to cases/PhasorDynamics/Toy/ThreeBusConstantSource.case.json is a bug fix we missed in previous PRs, and needed to make the case work here.
I'll update the CHANGELOG and rebase as this gets closer to ready-to-merge.

[superwhiskers]

looks good to me. i ran it on my machine and achieved similar numbers to those you got

[pelesh]

How come ratio is getting smaller for larger systems? It looks as if there is a scaling issue with Enzyme.

[lukelowry]

How come ratio is getting smaller for larger systems? It looks as if there is a scaling issue with Enzyme.

I believe most of that can be resolved by makin Branch have a manually defined Jacobian since it is linear. That brought down a lot of the Enzyme overhead on the large cases in my benchmarking