Hi! @bbbales2 and myself have found that the Adams Moulton solver in stan is very bad in terms of speed and accuracy in the problems we tried, see here https://github.com/stan-dev/math/pull/1641#issuecomment-642513156 for details. The example I tried is non-stiff which is supported by the observat…

[image] wds15: The tolerances in these examples is very low. There’s no “these”, it’s just one example, so I wouldn’t generalize, in particular [image] wds15: Is this a general thing to recommend with the Adams Moulten? I wonder if one really gets this high accuracy. Hos “low” is “low…

Whow…that was very constructive…so let’s park this simply.

Just tried this problem out in the new branch: rk45 timed: 179593 bdf timed: 203776 adams timed: 64780 And with the new interfaces: rk45 new timed: 161732 bdf new timed: 197372 adams new timed: 62082 So I tried the adams stuff on a version of the Lotka-Volterra case study and it was much slower …

[image] bbbales2: Is it obvious why that would be the case (can post code if that seems wrong)? For a same attainable order of accuracy and same time step, AM is more expensive because it’s implicit.

Well then why is RK45 slower in the problem above? And docs say the Adams-Moulton method will vary between 1st and 12th order.

Here’s another example, related to the orbital dynamics that @s.maskell mentioned here . In the ODE system(2body), I’m using the default adams/bdf tolerance, and Adams is faster than the other two. Then I changed the ODE system to a trivial linear one defined by identity matrix, and use a “very low” …

In this last model, let’s look at something that @charlesm93 had worked on. struct TwoCptNeutModelODE { template <typename T0, typename T1, typename T2> inline std::vector<typename stan::return_type<T1, T2>::type> operator()(const T0& t_in, const std::vector<T1>& x, …

In the context of a Stan program there is an implicit definition of very high and very low tolerance, since the problems should be scaled to unity scale roughly. Only then Stan programs work well. Or do you think that is not meaningful? You mention that it is a problem for rk45 to output at some sp…

[image] yizhang: The example is intended to demonstrate that without involving the nature of ODE system, talking about “high” & “low” tolerance is meaningless, let alone if an integrator “is useful”. If Stan can’t set these options automatically, then that leaves it to someone writing the mod…

Adams Moulton ODE solver in Stan useful?

General

yizhang June 15, 2020, 7:51pm 10

Because to attain the solution near t_0 and t_{\text{final}} rk45 needs to reduce time step aggressively, while AM doesn’t have to because it can enlist higher-order to reduce truncation error.

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Adams Moulton ODE solver in Stan useful?

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