Adaptivity in time

[fsimonis]

Currently, adaptivity is constrained to a single time window.

However, if a micro-simulation is not time-dependent (has no state), it is possible and highly beneficial to reuse simulation results from past iterations and time windows.

It could also be beneficial to load a database of pre-computed solutions on startup.
Also interesting could be to update such a cache with new simulation results during the simulation. This could make rerunning the simulation significantly faster.

[fsimonis]

I did some tinkering, and this is pretty easy to implement directly in the micro simulation. Of course, this is a rank-local solution. A naive cross-rank solution could just be a shared sqlite3 database.

For micro simulation $f(u, r) \mapsto (k, r)$, where u is input, k is output, and r is internal state, the micro simulation can use an rtree to store samples locally and query them with tolerance as such:

from rtree import index
global_index = index.Index(properties=index.Property(dimensions=2))

def query_cache(u, r, tol=1e-6):
    bbox = (u-tol, r-tol, u+tol, r+tol)
    for item in global_index.intersection(bbox, objects=True):
        return item.object
    return None

def insert_cache(u, r1, k, r2):
    global_index.insert(0, (u, r1, u, r1), (k, r2))

class MicroSimulation:
    # ...
    # self._r is state
    def solve(self, macro_data, dt):
        u = macro_data["u"]
        r = self._r

        # caching
        if hit := query_cache(u, r):
            k, self._r = hit
            return { "k": k }
        
        k, self._r = compute(u, r)

        # cache the result
        insert_cache(u, r, k, self._r)

        return {"k": k}