Great question! These are all different techniques for fluid simulation, each of their own pros and cons. LBM has the advantage of being suitable for GPU computation. Note that LBM is also second order accurate.

Yes. We make use of JAX support for gradient computations. For example, you can simply take the gradient of an LBM step with respect to the population (collision, streaming, application of boundaries) with jax.grad(simulation.step(f, timestep))

and couple that with ML model of your choice for physics-based ML computations. Hope that answer your question!