Description

Allow for specifying multiple initial conditions and solving in parallel using the IDAKLU solver

Motivation

Solving many simulations in parallel with different initial conditions is neccessary for implementing Unscented Kalman Filter or Particle Filter based parameter estimation methods, such as those currently being implemented in PyBOP (pybop-team/PyBOP#12). The IDAKLU solver currently has functionality for running multiple simulations with different parameters, but not for different initial conditions

Possible Implementation

How this is implemented would have to be discussed further, as currently the initial conditions are part of the model rather than the solver. Perhaps the solver could have an API for overriding the model y0 which allows for passing in either a column vector (single simulation) or a 2D array (n simulations where n is the number of columns)

Additional context

No response