[BradyPlanden]

Description

CasADi evaluated RegPower, and linear and pchip interpolants on a uniform grid, differently from evaluate. Both changes reach every user on the default CasADi path.

• RegPower:
  • evaluate computed x * (x² + δ²)^((a−1)/2) * scale^a, with x = base / scale, while CasADi computed x * hypot(x, δ)^(a−1) * scale^a, so the two rounded differently.
  • Both now evaluate one sequence of operations, RegPower._decomposition, each with its own sqrt, power and constants. The Python/JAX evaluator calls evaluate's form, whose _array_sqrt traces JAX arrays.
  • A literal exponent of 0.5 or 2 takes its powers as square roots (x / sqrt(sqrt(x² + δ²)) * sqrt(scale) for 0.5), so CasADi and evaluate agree bitwise, and for 0.5 the relative error stays below 6·2⁻⁵³.
  • With delta == 0, _decomposition returns power(base, exponent), so evaluate, JAX and CasADi all take the plain power. _function_diff and _function_jac differentiate base**exponent there too. Before, CasADi alone kept this fallback: evaluate gave NaN at base = 0 with exponent 0.5, and −16 rather than 16 at base = −4 with exponent 2, and the symbolic Jacobian disagreed with CasADi's values for negative bases.
  • The DiffSL export writes the pow form for every delta and exponent, unchanged.
  • Values move by round-off on both backends. _is_constant_value, which only the old CasADi form used, is removed.
• Interpolant lookup:
  • CasADi linear interpolants (on every axis, 1D to 3D) and 1D pchip interpolants find the segment holding x by binary search on every grid.
  • On a uniform grid they used CasADi's "exact" lookup. That can pick the neighbouring segment at a knot or one ulp beside it, and so put that segment's slope in the Jacobian. _is_uniform_grid is removed.
  • The pchip table stores each segment's left knot on every grid, so pchip values also move by round-off on uniform grids.
  • CasADi's cubic (B-spline) interpolant is unchanged.

#5959 lowers RegPower to Rust through the same _decomposition, and its parity tests hold Rust to these forms. This PR uses nothing from the Rust stack and can merge on its own.

Type of change

Bug fix, under ## Bug fixes in CHANGELOG.md.

Key checklist

• No style issues: pre-commit run
• Unit tests pass (N)
• Tests added: 9 Python tests. The lookup, bitwise and delta = 0 tests fail before this change.
  • CasADi MX and SX RegPower bitwise equal to evaluate, for exponents 0.5 and 2 at scales 1 and 33133;
  • RegPower at 0.5 against a 60-digit Decimal reference;
  • with delta = 0, values and the Jacobian against CasADi at base 0, −4 and 4, for exponents 0.5 and 2;
  • the segment CasADi picks at and one ulp either side of each knot of a uniform grid, by slope (linear) and curvature (pchip).

Rust execution engine stack: proposal #5667, showcase #5732

Each PR is one commit on the one above it.

#	PR	Adds
0	#5954	Function.create_copy keeps the function's class
0b	#5955	CasADi's RegPower and uniform-grid interpolant lookups match evaluate ← this PR
1	#5956	pybamm-core: expression graph, typed IR, interpreters, forward-mode AD
2	#5957	pybamm-core: CompiledModel, coloured Jacobians, the C ABI
3	#5958	pybamm.rust bindings, built into the pybamm wheel
4	#5959	Symbol.to_rust
5	#5960	convert_to_format = "rust" for ScipySolver, AlgebraicSolver and EIS
6	#5961	pybammsolvers: IDAKLU over the C ABI
7	#5962	IDAKLUSolver on rust models
8	#5963	variables and sensitivities read in Rust
9	#5964	pybamm-core: diffsol DAE solver
10	#5965	pybamm.DiffsolSolver
11	#5966	"rust" as the default convert_to_format

[codecov]

Codecov Report

❌ Patch coverage is 83.87097% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.23%. Comparing base (743663a) to head (a72301b).

Files with missing lines	Patch %	Lines
...ges/pybamm/src/pybamm/expression_tree/functions.py	80.76%	5 Missing ⚠️

Additional details and impacted files

@@                      Coverage Diff                       @@
##           stack/00-function-copy-fix    #5955      +/-   ##
==============================================================
- Coverage                       98.25%   98.23%   -0.02%     
==============================================================
  Files                             350      350              
  Lines                           36109    36104       -5     
==============================================================
- Hits                            35478    35468      -10     
- Misses                            631      636       +5     

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Bencher Report

Project	PyBaMM
Branch	stack/00b-casadi-numerics-fix
Testbed	bare-metal

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[MarcBerliner]

Is there anything simple we can do to keep the exact lookups? It's not a big deal but it'd be nice to use them if we can instead of the slower binary search