Solvers Overview

PyBaMM provides several solver backends suited to different model types and performance requirements. This page compares the available solvers and explains how to choose the right one.

Solver Comparison

Solver	Backend	ODE	DAE	Sensitivity	Notes
CasadiSolver	CasADi / SUNDIALS	Yes	Yes	Yes	General-purpose; safe mode handles events
IDAKLUSolver	SUNDIALS IDA + KLU	Yes	Yes	Yes	Fastest for most problems; recommended default
ScipySolver	SciPy solve_ivp	Yes	No	No	Simple; no DAE support
JaxSolver	JAX	Yes	BDF only	No	GPU/TPU capable; requires Python ≥ 3.11
AlgebraicSolver	SciPy root-finding	No	Algebraic only	No	For purely algebraic (steady-state) problems
CompositeSolver	Multiple backends	Yes	Yes	Varies	Tries multiple solvers until one succeeds
CasadiAlgebraicSolver	CasADi	No	Algebraic only	No	CasADi-based algebraic solver

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Choosing a Solver

• Most lithium-ion models (SPM, SPMe, DFN) include algebraic equations (DAEs). Use IDAKLUSolver (default in pybamm.Simulation) for best performance.
• Drive-cycle simulations with no voltage events: use CasadiSolver(mode="fast") or IDAKLUSolver.
• Simple ODE-only models (equivalent circuit, 0D): ScipySolver works well and has minimal dependencies.
• Batch parameter sweeps on GPU/TPU: JaxSolver with method="RK45" enables JIT compilation.

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BaseSolver Common Interface

All solvers inherit from pybamm.BaseSolver and share the following constructor parameters and methods.

Constructor Parameters

method · str · default: "None"

Integration method name. Meaning is solver-specific.

rtol · float · default: "1e-6"

Relative tolerance.

atol · float · default: "1e-6"

Absolute tolerance.

root_method · str | algebraic solver · default: "None"

Method used to compute consistent initial conditions for DAE problems. Options include "casadi", "lm", "hybr", or a PyBaMM algebraic solver class.

root_tol · float · default: "1e-6"

Tolerance for the initial-condition root-finding step.

extrap_tol · float · default: "-1e-10"

Tolerance for detecting extrapolation beyond the solved time span.

on_extrapolation · str · default: "\"warn\""

Behaviour when extrapolation is detected. One of "warn", "error", or "ignore".

output_variables · list[str] · default: "[]"

If specified, only these variables are computed and returned (reduces memory usage).

solve

solver.solve(model, t_eval, inputs=None, initial_conditions=None, ...)

Solve the model over the time span t_eval and return a pybamm.Solution object.

step

solver.step(old_solution, model, dt, npts=2, inputs=None, ...)

Advance the solution by a single time step dt. Useful for online / real-time simulation.

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Setting Tolerances

import pybamm

# Tighter tolerances for high-accuracy simulations
solver = pybamm.IDAKLUSolver(rtol=1e-8, atol=1e-8)

# Looser tolerances for fast exploratory runs
solver = pybamm.CasadiSolver(rtol=1e-3, atol=1e-6)

sim = pybamm.Simulation(
    pybamm.lithium_ion.DFN(),
    solver=solver,
    parameter_values=pybamm.ParameterValues("Chen2020"),
)
sol = sim.solve([0, 3600])

For production simulations with lithium-ion physics models, IDAKLUSolver is the recommended starting point. It handles both ODE and DAE systems, supports sparse KLU factorisation, and exposes a rich options dict for fine-tuning.