A pattern database (PDB) is a heuristic function implemented as a lookup table. It stores the lengths of optimal solutions for instances of subproblems. Most previous PDBs had a distinct entry in the table for each subproblem instance. In this paper we apply learning techniques to compress PDBs by using neural networks and decision trees thereby reducing the amount of memory needed. Experiments on the sliding tile puzzles and the TopSpin puzzle show that our compressed PDBs significantly outperforms both uncompressed PDBs as well as previous compressing methods. Our full compressing system reduced the size of memory needed by a factor of up to 63 at a cost of no more than a factor of 2 in the search effort.