[v14 ready] Tutorial for ensuring performance for ODE simulations #751

TorkelE · 2023-12-25T14:49:17Z

Creates a new doc page, providing some performance advice for ODE simulations. Stuff covered:

Stiff vs non-stiff ODEs.
Selecting a solver for ODE simualtions.
Various options for Jacobian computations (symbolic jacobian, sparse jacobian, lienar solver selection, and preconditioners).
Parallelisation on CPUs.
Parallelisation on GPUs.

The GPU parallelization part is not ready, I have only started. However, I need to go through some stuff with Utkarsh before finishing that part.

Also, if someone have a link to a good reference book introducing this kind of stuff, that would be useful

docs/src/catalyst_applications/ode_simulation_performance.md

ChrisRackauckas · 2024-01-05T14:19:27Z

docs/src/catalyst_applications/ode_simulation_performance.md

+When implicit solvers use e.g. the Newton-Raphson method to, in each simulation time step, solve a (typically non-linear) equation, they actually solve a linearised version of this equation. For this they use a linear solver, the choice of which can impact performance. To specify one, we use the `linsolve` option (given to the solver function, *not* the `solve` command). E.g. to use the `KLUFactorization` linear solver we run
+```@example ode_simulation_performance_3
+using DifferentialEquations
+solve(oprob, Rodas5P(linsolve = KLUFactorization()))


This is the wrong solver for anything of this size and we should demonstrate this more correctly.

We should recommend using MKL and trying UMFPACK

You mean that Rodas5P is wrong for large problems (where we would do something like this) and should be changed, or that since preconditioners and stuff like this is not good for a 2-state brusselators we should demonstrate on a larger model?

Didn't find any examples for MKL, so was unsure on how to implement it here.

ChrisRackauckas · 2024-01-05T14:20:24Z

docs/src/catalyst_applications/ode_simulation_performance.md

+```
+Next, `incompletelu` can be supplied to our solver using the `precs` argument:
+```@example ode_simulation_performance_3
+solve(oprob, Rodas5P(precs = incompletelu))


this won't use the preconditioner

ChrisRackauckas · 2024-01-05T14:20:51Z

docs/src/catalyst_applications/ode_simulation_performance.md

+```
+Finally, we note that since matrix-free linear solvers (like `KrylovJL_GMRES`) by default do not build a Jacobian. Hence, if we want to use them with a preconditioner we must tell them to build it. This can be done using the `concrete_jacobian=true` option:
+```@example ode_simulation_performance_3
+solve(oprob, Rodas5P(linsolve = KrylovJL_GMRES(), precs = incompletelu, concrete_jac=true))


you need to skip straight to here because the line above is just incorrect

Does preconditioners make sense for linear solvers except for KrylovJL_GMRES then? Or should concrete_jac=true be used for the previous case?

docs/src/catalyst_applications/ode_simulation_performance.md

isaacsas · 2024-01-05T14:23:48Z

Why don’t we just use some of the examples from the Catalyst paper that show different performance characteristics to illustrate which solvers and configurations work best in different cases? Then we’ve already done the benchmarking and know what is fastest.

docs/src/catalyst_applications/ode_simulation_performance.md

TorkelE · 2024-01-05T16:24:41Z

Thanks for the input! I'm a little bit uncertain how to deal with the precondition part, but otherwise all good.

TorkelE · 2024-01-09T22:44:30Z

Did you have any further input on the preconditioners @ChrisRackauckas?

Also, what is the progress on moving default solvers to OrdinaryDiffEq? If that is coming soon then useful, but it would be useful to have a quick and dirt solver selection advice that did not depend on reading through all the doc, nor loading the full DifferenitalEquations suite.

Co-authored-by: Christopher Rackauckas <[email protected]>

TorkelE changed the title ~~Tutorial for ensuring performance for ODE simualtions~~ [WIP] Tutorial for ensuring performance for ODE simulations Dec 25, 2023

TorkelE changed the title ~~[WIP] Tutorial for ensuring performance for ODE simulations~~ Tutorial for ensuring performance for ODE simulations Dec 27, 2023

utkarsh530 reviewed Jan 4, 2024

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