[AnonNo15]

I can answer the "why" question. Provided, our descendants will be able to empathize with their ancestors (rather big "if"), they can use the simulation to reverse the death and resurrect every person who ever lived.

As for verifying the accuracy of the simulation, you only need information about the initial state of the universe (think CMB radiation) and partial information about past states of the universe to reproduce a selected region of universe with certain level of precision.

[teraflop]

You're using words like "only", "partial" and "a selected region" but you're still talking about staggering amounts of information, on any humanly achievable scale.

A single human body contains on the order of 10^27 atoms. If you just wanted to record the state of someone's mind, with sufficient fidelity to be worthy of the term "resurrection", you could probably get away with a coarser granularity. But you're talking about accurately simulating a chaotic system, which means you need extreme precision to prevent the simulation from diverging.

More to the point, it's unlikely that the information you're seeking still exists, even in principle. Think about Conway's Game of Life; the rules are injective, meaning many different initial states can lead to the same final state. An being who lived in the Game of Life would never be able to precisely reconstruct its history with any level of technology, because there would be an astronomical number of equally possible predecessor states. (As far as we know, our universe is continuous, not discrete, but the laws of thermodynamics have a similar effect.)

[AnonNo15]

None of the above needs to happen overnight. Who knows what humanity will be capable of in 1000 years?

Furthermore, in a strict sense my question would be 'Is it possible to extract additional information with any degree of certainty about the past state of some region of the universe, using simulation algorithms and partial information about past states of this region?'

This assumption doesn't need to go to the atomic level on the first try. If you can replicate distribution of mass on the scale of galaxy clusters as compared to the present day using the above approach, it would certainly prompt further research in this area.

[caf]

Regarding your last point, it is my understanding that in fact the laws of physics are entirely time-reversible in a mathematical sense, and that what thermodynamics does on top of that is say "in reality, time runs only in this direction".