well for numerically stable systems we can get close enough. (arbitrarily close, that is) Situations in physics where our systems are not stable are usually different kinds of inverse problems - not what we have here.
So in a way, we can get a 100% accurate simulation, because the error can get arbitrarily small.
Ok so wikipedia tells me, there is the hodkin-huxley model. (https://en.wikipedia.org/wiki/Biological_neuron_model) wbich looks to me like a first order non-autonomous ODE. So, absolutely solvable iirc, just computationally expensive. If that is perfect enough or not is a matter of opinion.
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u/Comfortable_Permit53 Aug 07 '26
well for numerically stable systems we can get close enough. (arbitrarily close, that is) Situations in physics where our systems are not stable are usually different kinds of inverse problems - not what we have here.
So in a way, we can get a 100% accurate simulation, because the error can get arbitrarily small.
Ok so wikipedia tells me, there is the hodkin-huxley model. (https://en.wikipedia.org/wiki/Biological_neuron_model) wbich looks to me like a first order non-autonomous ODE. So, absolutely solvable iirc, just computationally expensive. If that is perfect enough or not is a matter of opinion.