Reverse problem

Modelling systems, mostly useful in computing properties, is often done as a forward problem, which means calculating something from first principles. This is how science has always worked: abstract the problem as much as possible until it becomes useful to make a prediction.

On the other hand, we can reverse the question: what is the starting point for a given output?

A trivial thing: at what time do I have to leave to arrive on time?

As problems get more complex, the reverse problem becomes intractable. This is a crucial aspect of cryptography: it's trivial to encode something, but impossible to decode without the key (Physical Unclonable Function are in the same train of thought).

Specifically, material discovery often relies on using DFT, a powerful (and complete) numerical method to calculate molecular behaviour. Lot's of work has been put into calculating properties based on DFT modelling (which is not at all a trivial step).

There are entire databases with modelled systems and interactions ([[@abed2024Open Catalyst Experiments 2024 (OCx24): Bridging Experiments and Computational Models|Open Catalyst Experiments 2024 (OCx24): Bridging Experiments and Computational Models]], for example).

But those still work forward with experimental validation.

What if we ask ourselves: "How do I make a material that has X, Y, Z properties, with W boundary conditions?"

The problem is intractable today.

I believe that tackling the reverse problem with quantum computers will be the true breakthrough and in the meantime we need to leverage what we can, including AI for the reverse problem.