Sure we can only approximate, but why wouldn't those approximations be sufficient? We were able to solve the n-body problem with sufficient accuracy for Voyage

Sure we can only approximate, but why wouldn't those approximations be sufficient? We were able to solve the n-body problem with sufficient accuracy for Voyager to successfully encounter and gravity-slingshot around Jupiter twice and every other outer planet, with only the computing power available in 1977. The mechanism of action of a neuron is not very complex. It follows the all-or-none principle along with an activation potential which is easily emulated in a binary circuit. It does have additional chemical inputs which can raise or lower activation potential. The only difficult part is sufficient connectivity, but we can simulate that, no need to use an FPGA to get actual connectivity. Modern transistors are super-fast and super-small compared to neurons so you have quite a bit of room to sum inputs, check activation energy, check chemical levels, and lookup + signal the 'connected' neurons.