[FFroehlich]

Fixes #3377.
Fixes #3384.
Fixes #3389.
Supersedes #3379.

Problem

Noise formulas (sigmay/sigmaz) that reference expressions (w), e.g., targets of SBML assignment rules, passed import but produced uncompilable code:

dsigmaydp.cpp:12:28: error: 'readout_' was not declared in this scope

The generated sigmay(t, p, k, y) / sigmaz(t, p, k) functions (and JAX _sigmay(y, p, np)) do not receive w. DEModel only checked sigmas for states, so expressions went straight to code generation. As a consequence, dsigmaydp was also wrong, since it lacked the parameter dependence of the expression. This also affected expressions that depend only on parameters (#3377, e.g., sigma = s with s := 0.1 * p) and event noise formulas.

Related cases that were accepted at import but did not compile (#3389): noise formulas with piecewise functions (no Heaviside argument h), splines (no spline values), and state-dependent event noise formulas (states were replaced by the event output z, but sigmaz has no z argument).

Changes

In DEModel._compute_equation, post-processing of sigmay/sigmaz:

• Expressions in sigmas are replaced by their (recursively expanded) definitions. For sigmay, the observable equation that the existing state elimination solves for the state is expanded the same way. sigma = sd*readout with obs = readout, readout := A now becomes sd*obs; with obs = scale*readout it becomes sd*obs/scale.
• States in sigmaz are no longer replaced by the event output, since sigmaz is evaluated without it (Noise formulas with piecewise functions, splines, or state-dependent event noise formulas generate non-compiling code #3389, point 3). State-dependent event noise formulas, and event noise formulas that refer to the event observable itself, are now rejected at import.
• The final check reports every symbol that is not available for sigma evaluation, not only states that could not be eliminated: Heaviside/event indicators (h, Noise formulas with piecewise functions, splines, or state-dependent event noise formulas generate non-compiling code #3389 point 1), spline values (spl, Noise formulas with piecewise functions, splines, or state-dependent event noise formulas generate non-compiling code #3389 point 2), conservation law totals (tcl), and, for sigmaz, the event observables. These now fail at import with an informative message instead of failing in the compiler. All of these cases were compile errors before, so nothing that worked before is rejected now.

The fix lives in DEModel, so it covers the SBML and PySB importers and both the C++ and JAX backends.

Notes for reviewers

• The error message for unsupported sigmas changed (the old wording, "State-dependent observables are not supported", was misleading). Offending symbols are listed sorted by name, so the message is deterministic. For SBML import, it still reaches users as the __cause__ of the generic SBMLException raised in sbml2amici; I left that wrapping unchanged.
• The expansion substitutes only the w symbols that actually occur, until none remain, instead of using smart_subs_dict over all of w. That avoids O(n_w) or O(n_w²) substitution work for large models.
• test_sigma_depending_on_assignment_rules runs with rtol=atol=1e-12. The sigmas there are small and proportional to the observable, so at default tolerances the integration error (~4e-7 relative in the state) is amplified enough to make the finite-difference check miss by ~1e-4. At tight tolerances, FSA, ASA, and finite differences agree to ~1e-9.
• CI: PEtab Testsuite (3.14) failed on earlier commits of this PR, as it did on main, because libpetab-python#545 changed how numeric overrides are serialized (test_flatten_timepoint_specific_output_overrides). This was fixed on main by Fix flattened observable IDs in PEtab v2 test #3394, which is now merged into this branch.

Testing

New tests in python/tests/test_sbml_import.py:

• test_sigma_depending_on_assignment_rules (Noise formula referencing an assignment-rule parameter generates uncompilable sigmay code #3384): simulated sigmay values and FSA/ASA gradient checks for sigmas referencing state- and parameter-dependent assignment rules. It also checks that a sigma whose state cannot be expressed in terms of the observable is rejected, both without conservation laws and with them, where the conservation law total remains. Conservation laws for non-constant species are enabled explicitly, so the test does not depend on GITHUB_ACTIONS.
• test_noise_formula_with_expression (Generated code does not compile if a noise formula refers to an expression #3377, adapted from Fix noise formulas that refer to model expressions #3379): sigmay, ssigmay, and sigmaz for time-resolved and event noise formulas that refer to expressions, including a state-dependent one for sigmay.
• test_unsupported_sigmas_rejected (Noise formulas with piecewise functions, splines, or state-dependent event noise formulas generate non-compiling code #3389): piecewise functions, splines, and event noise formulas depending on states or on the event observable itself are rejected at import with a message naming the offending symbol.

Locally, the sigma-related tests in test_sbml_import.py pass with GITHUB_ACTIONS=true. The local AMICI build predates the latest C++ changes on main, which do not affect these tests; the full suite runs on CI.

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4 open findings

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What changed in this PR

Fixes SBML-imported models producing uncompilable code when sigmay/sigmaz reference assignment-rule expressions (w) by expanding those expressions during equation computation and rejecting unsupported dependencies earlier.

Changes:

• Expand w (assignment-rule/expression) symbols inside sigmay/sigmaz and related observable/event-observable equations during _compute_equation.
• Improve validation and error reporting for sigma dependencies that cannot be evaluated (states not eliminable to the respective observable, plus tcl/h/spl).
• Add a regression test covering sigma formulas depending on assignment rules (including parameter-only rules) and gradient checks.

File	Description
python/​sdist/​amici/​_symbolic/​de_model.py	Substitutes w symbols in sigmas/observables and reports unavailable symbols with a clearer import-time error.
python/​tests/​test_sbml_import.py	Adds regression test for assignment-rule-dependent sigmas, validates rejection and correct sigma/gradient behavior.
changelog.d/​+sigma-expressions.fix.md	Documents the fix and the new import-time rejection behavior for unsupported sigma dependencies.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 80.08%. Comparing base (a11074a) to head (ae8ccf7).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3388      +/-   ##
==========================================
+ Coverage   80.06%   80.08%   +0.02%     
==========================================
  Files         320      320              
  Lines       22680    22691      +11     
  Branches     1531     1531              
==========================================
+ Hits        18158    18173      +15     
+ Misses       4514     4510       -4     
  Partials        8        8              

Flag	Coverage Δ
cpp	74.20% <100.00%> (+0.03%)	⬆️
cpp_python	35.10% <68.18%> (+0.02%)	⬆️
petab	48.48% <68.18%> (+0.02%)	⬆️
petab_sciml	16.91% <63.63%> (+0.03%)	⬆️
petab_sciml_benchmarks	15.49% <63.63%> (+0.04%)	⬆️
python	72.35% <100.00%> (+0.03%)	⬆️
sbmlsuite	51.02% <ø> (ø)

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Files with missing lines	Coverage Δ
python/sdist/amici/_symbolic/de_model.py	93.82% <100.00%> (+0.30%)	⬆️

... and 1 file with indirect coverage changes

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[dweindl]

Looks good. Also closes #3377. Addresses points 1 & 2 of #3389 -- also add the last point? Either is fine. Supersedes #3379.