Description

This PR updates the CasadiAlgebraicSolver with three key improvements:

Caches the root solver:

• This makes a cached and reusable version of the root solver generated by casadi, which works for different values of time, initial values of the differential states, and input parameters. This reduces the runtime of the DFN by ~6.5% in the example below.

Added a step_tol parameter:

• This sets the tolerance for the Newton iteration step norm and defaults to 1e-4 (equal to IDA's rtol). Previously, the casadi rootfinder used a much tighter default of 1e-12, which caused issues. That strict value made it harder for the line search algorithm to pick a good step size, often leading to solver failure. By relaxing step_tol, the solver is now more robust, typically requires fewer iterations to converge, and adds minimal error to the solve

Improved convergence criterion:

• The solver now uses casadi’s success flag and adds a safeguard to ensure the solution doesn’t contain nan or inf values

Fixes #4952

Example:

import pybamm
from tqdm import tqdm

experiment = pybamm.Experiment(
    [
        (
            "Discharge at C/10 for 10 hours or until 3.3 V",
            "Rest for 1 hour",
            "Charge at 1 A until 4.1 V",
            "Hold at 4.1 V until 50 mA",
            "Rest for 1 hour",
        )
    ]
    * 3,
)
model = pybamm.lithium_ion.DFN()
sim = pybamm.Simulation(model, experiment=experiment, solver=pybamm.IDAKLUSolver())
sim.solve()

time = 0
repeats = 100
timer = pybamm.Timer()
for i in tqdm(range(repeats)):
    timer.reset()
    sol = sim.solve()
    time += timer.time()
print(time / repeats)

# Time (new): 327.475 ms
# Time (old): 349.887 ms

Type of change

Please add a line in the relevant section of CHANGELOG.md to document the change (include PR #)

Important checks:

Please confirm the following before marking the PR as ready for review:

• No style issues: nox -s pre-commit
• All tests pass: nox -s tests
• The documentation builds: nox -s doctests
• Code is commented for hard-to-understand areas
• Tests added that prove fix is effective or that feature works