Points interpolation on a polygon geometry

I would like to know how to interpolate point data on a polygon geometry.

I have two PostGIS tables:

• the first one contains hourly rain values evaluated in the nodes of a regular grid (specified in a column with POINT type geometry)
• the second one contains other values associated with the triangles of an irregular grid (specified in a column with POLYGON type geometry)

I would like to interpolate the hourly rain values (first table) on the polygons of the irregular grid (second table); then, I would like to save the results in the second table.

Is there a way to do this using some PostGIS functions?

I may use the IDW method, but it is only an hypothesis.