Consistent Jacobian tangent (unwrap-before-differentiate fix) — opt-in, default-off by lmoresi · Pull Request #258 · underworldcode/underworld3

lmoresi · 2026-06-19T10:35:34Z

Consistent Jacobian tangent for nonlinear (viscoplastic) solves — opt-in, default-off

The bug

SNES Jacobian assembly differentiated the residual flux F1 while the effective
viscosity was still a wrapped UWexpression atom, so ∂η/∂(grad v) was silently dropped
from every Jacobian. UW3 viscoplastic Stokes was therefore running an accidental Picard /
defect-correction tangent, not full Newton — the unwrap happened after the derivative
instead of before it. Constant-viscosity problems were unaffected, which is why it stayed
hidden behind the "≈20 Picard iterations is intrinsic" folklore.

The fix (default-off, bit-identical by default)

symbolic_keep_constants unwrap mode — expands UWexpression atoms down to (but not
including) truly-constant atoms (η₀, τ_y stay symbolic for the constants[] mechanism).
The keep-symbolic predicate is the same _is_truly_constant used by constants[]
extraction, so they cannot drift (drift-guard test).
solver.consistent_jacobian: False (default, frozen/Picard, bit-identical) /
True (full Newton) / "continuation" (Picard→Newton via an α-blend routed through
constants[], so switching costs no JIT recompile and α=0 is bit-identical).
Constitutive_Model.flux_jacobian hook (default None) for a model to supply a smooth
tangent law; _newton_flux is guarded so the default path never evaluates it.

The residual never goes through the new path, so a converged solution always satisfies the
exact constitutive law.

Non-regression evidence

Constant-viscosity Jacobian symbolically bit-identical (0/N blocks change).
test_1010, SolCx test_1015, test_0610, asymmetric-Jacobian guard, units (64) pass;
level_1 tier_a 225/225.
Crash-isolated (--forked) level_2 tier_a failure set is identical to pristine
development — the pre-existing reds (test_1012 gmsh crash + 3 test_1052 VEP) are not
introduced here.

Scope / why a smooth Jacobian is not the VEP fix

For a hard-Min residual, a smooth Jacobian is the consistent tangent of a different
(harmonic) problem — it diverges more than Picard. The robust route for hard-yield VEP is
problem-space homotopy (ramp the softmin softness δ→0; δ=0 is identically Min), which is
a separate follow-up PR that reuses this PR's constants[]-ramp machinery. See
docs/developer/design/jacobian-consistent-tangent.md for the full tangent hierarchy and the
successor plan.

Underworld development team with AI support from Claude Code

Gated behind consistent_jacobian (default False = bit-identical Picard). - symbolic_keep_constants unwrap mode (constants[]-safe, drift-guarded) - consistent_jacobian: False | True | 'continuation' (alpha-blend via constants[]) - model-owned flux_jacobian hook; Nitsche bd_F1 wired Validated: level_1 tier_a 225/225, units 64/64, constant-visc bit-identical. Underworld development team with AI support from Claude Code

Creating the continuation alpha UWexpression in every solver __init__ bumped the global unique-name counter, shifting JIT cache keys enough to flip two known-flaky VEP variable-dt yield-lock tests in full-suite runs. Construct alpha lazily (continuation mode only) so the default Picard path creates no extra expression. Verified: level_2 tier_a forked failure set now IDENTICAL to pristine origin/development (4 pre-existing failures). Underworld development team with AI support from Claude Code

…n-unwrap-to-constants # Conflicts: # src/underworld3/cython/petsc_generic_snes_solvers.pyx

…owned) ViscoElasticPlasticFlowModel.flux_jacobian returns the flux with Min->harmonic (1/(1/eta_ve+1/eta_pl)) and Max smoothed, for the Jacobian source ONLY (exact Min residual preserved). Pure symbolic substitution on the live flux — no state mutation (fixes the earlier err-77 from a yield_mode toggle hack). Runs clean. Guard _newton_flux on consistent_jacobian so the default (Picard) path never evaluates flux_jacobian — keeps default assembly allocation-free / bit-identical (test_1010 6/6). NOTE: smooth-Jacobian + hard-Min residual is an inconsistent tangent and does NOT improve convergence on the BDF-2 VEP loading test (8/15 vs Picard 3/15); only full harmonic (consistent smooth residual+Jacobian) converges (0/15). The hook is correct, clean, and available; VEP convergence remains a separate issue. Underworld development team with AI support from Claude Code

The smooth-Jacobian-with-Min-residual tangent is inconsistent (consistent with the harmonic problem, not Min) and converges worse than Picard on hard-yield VEP — so the VEP-specific harmonic flux_jacobian override is deferred to the yield-law / delta-homotopy follow-up PR. The generic Constitutive_Model. flux_jacobian hook (default None) + the _newton_flux guard remain. Add docs/developer/design/jacobian-consistent-tangent.md: the bug, the opt-in/default-off fix, non-regression evidence, the tangent hierarchy, and the delta-homotopy successor work. Underworld development team with AI support from Claude Code

Copilot

Pull request overview

This PR introduces an opt-in “consistent Jacobian tangent” path for nonlinear/viscoplastic SNES solves by unwrapping UWexpression atoms before symbolic differentiation (while still preserving truly-constant atoms for the PETSc constants[] mechanism). It also adds a continuation mode to blend Picard→Newton without triggering JIT recompiles, plus a constitutive-model hook to provide a custom Jacobian-only flux.

Changes:

Add symbolic_keep_constants unwrapping mode to expand non-constant UWexpression atoms while preserving truly-constant atoms as the same symbols for constants[].
Add solver.consistent_jacobian with modes False (default Picard), True (Newton), and "continuation" (alpha-blended Picard→Newton).
Add Constitutive_Model.flux_jacobian hook (default None) so models can supply a Jacobian-only surrogate flux.

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 9 comments.

File	Description
`src/underworld3/function/expressions.py`	Adds `symbolic_keep_constants` unwrapping mode used to expose coefficient dependence during Jacobian differentiation without breaking `constants[]`.
`src/underworld3/cython/petsc_generic_snes_solvers.pyx`	Implements Jacobian source selection (Picard/Newton/continuation), uses unwrap-before-differentiate for Jacobian assembly, and adds continuation solve control flow.
`src/underworld3/constitutive_models.py`	Introduces `flux_jacobian` optional hook for Jacobian-only tangent substitution and documents intended usage.
`docs/developer/design/jacobian-consistent-tangent.md`	New design note explaining the unwrap-before-differentiate bug, the opt-in fix, and the tangent/continuation rationale.

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+    if isinstance(expr, sympy.NDimArray):
+        return sympy.Array([f(e) for e in expr], expr.shape)
+    return f(expr)  # scalar expression


+    This is a no-op for constant-viscosity problems (eta has no grad-v
+    dependence), so those Jacobians stay bit-identical.
+
+    See ``docs/developer/design/jacobian-unwrap-constants-bug.md``.


+        # the model's own smooth law (constitutive_model.flux_jacobian) when it
+        # provides one; otherwise the exact unwrapped flux.
+        #
+        # See docs/developer/design/jacobian-unwrap-constants-bug.md.


+        # The residual fns above (self._u_F0/_u_F1/_p_F0) are left untouched —
+        # getext() unwraps those itself. For constant-viscosity problems this
+        # is a no-op (eta has no grad-v dependence) so the Jacobian is
+        # bit-identical. See docs/developer/design/jacobian-unwrap-constants-bug.md


+        # Restore a clean Picard tangent for any subsequent solve (next step).
+        self._set_newton_alpha(0.0)
+


+        if self.consistent_jacobian == "continuation":
+            self._continuation_solve(gvec, verbose=verbose)
+        else:
+            self.snes.solve(None, gvec)
        if divergence_retries <= 0:
            return


+        Returns ``None`` by default, meaning the solver differentiates the
+        exact :attr:`flux` (the Newton fix unwraps it first; a generic Min/Max
+        kink-smoothing fallback then rounds any remaining yield kink).


+    # (ramp the softmin softness δ→0), not a smooth tangent. See the design doc
+    # docs/developer/design/jacobian-unwrap-constants-bug.md. The generic


+        # JACOBIAN: unwrap (keep constants) + smooth Min/Max kinks so the
+        # derivative sees the field-dependence of any nonlinear coefficient
+        # (full Newton) while the residual keeps the exact form. No-op for
+        # constant coefficients -> bit-identical. See _jacobian_source.


bknight1 · 2026-06-25T14:47:01Z

@lmoresi I've had a look at this PR and it's vastly improved the convergence of the VP models I've been working on, both when using continuous and True. The only issue is compilation time with multimaterials, which can be >5 mins, with 'continuous' taking longer than True. Another issue is the compilation appears to occur twice after updating the constitutive model (one to check the hash is different then a rebuild the jacobians).

I have made some modifications to fix these issues, happy to discuss committing these changes.

lmoresi added 5 commits June 18, 2026 16:55

Merge remote-tracking branch 'origin/development' into bugfix/jacobia…

d7e0cd4

…n-unwrap-to-constants # Conflicts: # src/underworld3/cython/petsc_generic_snes_solvers.pyx

Copilot AI review requested due to automatic review settings June 19, 2026 10:35

Copilot started reviewing on behalf of lmoresi June 19, 2026 10:36 View session

Copilot AI reviewed Jun 19, 2026

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lmoresi mentioned this pull request Jun 24, 2026

Nitsche free-slip BC: inconsistent Jacobian for anisotropic (transverse-isotropic) constitutive models #239

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Consistent Jacobian tangent (unwrap-before-differentiate fix) — opt-in, default-off#258

Consistent Jacobian tangent (unwrap-before-differentiate fix) — opt-in, default-off#258
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		# Restore a clean Picard tangent for any subsequent solve (next step).
		self._set_newton_alpha(0.0)

		# (ramp the softmin softness δ→0), not a smooth tangent. See the design doc
		# docs/developer/design/jacobian-unwrap-constants-bug.md. The generic

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lmoresi commented Jun 19, 2026

Consistent Jacobian tangent for nonlinear (viscoplastic) solves — opt-in, default-off

The bug

The fix (default-off, bit-identical by default)

Non-regression evidence

Scope / why a smooth Jacobian is not the VEP fix

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Reviewed changes

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bknight1 commented Jun 25, 2026

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