Well, Joseph Nagyvary is a Ph.D in chemistry, and he has come quite close to figuring out how Stradivarius did it.
He discovered that using wood treated with borax, ground crystals, and fruit gums made a violin that sounded more like a Strad. He says Stradivari used these things to prevent insects and mold, but that he may not have realized what a good effect it would have on the sound.
In terms of the physical dimensions, laser x-ray technology has helped to reproduce that. But a violin is said to have more than 50 parts, and exploring every one of the variables there could take another 200 years.
Overall, people have come close, but no one has found all the secrets yet.