[Question] How should we model complex systems?

By “com­plex”, I mean a sys­tem for which it would be too com­pu­ta­tion­ally costly to model it from first prin­ci­ples e.g. the econ­omy, the cli­mate (my field, by the way). Sup­pose our goal is to pre­dict a sys­tem’s fu­ture be­havi­our with min­i­mum pos­si­ble er­ror given by some met­ric (e.g. min­imise the mean square er­ror or max­imise the like­li­hood). This seems like some­thing we would want to do in an op­ti­mal way, and also some­thing a su­per­in­tel­li­gence should have a strat­egy to do, so I thought I’d ask here if any­one has worked on this prob­lem.

I’ve read quite a bit about how we can op­ti­mally try to de­duce the truth e.g. ap­ply Bayes’ the­o­rem with a prior set fol­low­ing Ock­ham’s ra­zor (c.f. Solomonoff in­duc­tion). How­ever, this seems difficult to me to ap­ply to mod­el­ling com­plex sys­tems, even as an ideal­i­sa­tion, be­cause:

  1. Since we can­not af­ford to model the true equa­tions, ev­ery mem­ber of the set of mod­els available to us is false, so the like­li­hood and pos­te­rior prob­a­bil­ity for each will typ­i­cally eval­u­ate to zero given enough ob­served data. So if we want to use Bayes’ the­o­rem, the prob­a­bil­ities should not mean the prob­a­bil­ity of each model be­ing true. But it’s not clear to me what they should mean—per­haps the prob­a­bil­ity that each model will give the pre­dic­tion with the low­est er­ror? But then it’s not clear how to do up­dat­ing, if the nor­mal like­li­hoods will typ­i­cally be zero.

  2. It doesn’t seem clear that Ock­ham’s ra­zor will be a good guide to giv­ing our mod­els prior prob­a­bil­ities. Its use seems to be mo­ti­vated by it work­ing well for de­duc­ing fun­da­men­tal laws of na­ture. How­ever, for mod­el­ling com­plex sys­tems it seems more rea­son­able to me to give more weight to mod­els that in­cor­po­rate what we un­der­stand to be the im­por­tant pro­cesses—and past ob­ser­va­tions can’t nec­es­sar­ily help us tell what pro­cesses are im­por­tant to in­clude, be­cause differ­ent pro­cesses may be­come im­por­tant in fu­ture (c.f. biolog­i­cal feed­backs that may kick in as the cli­mate warms). This could per­haps be done by hav­ing a strat­egy for de­riv­ing ap­prox­i­mate af­ford­able mod­els from the fun­da­men­tal laws—but is it pos­si­ble to say any­thing about how an agent should do this?

I’ve not found any­thing about ra­tio­nal strate­gies to ap­prox­i­mately model com­plex sys­tems rather than de­rive true mod­els. Thank you very much for any thoughts and re­sources you can share.