This is because the problem of connecting scales is much more general than just the quantum to the classical there’s also connecting the scale of molecules to proteins and proteins to cells and cells to organs and so on. Same in chemical engineering and climate simulations.
I think neural network potentials are the most important scientific tool of the next decade. The ability to simulate systems at the molecular scale starting from nothing but quantum mechanics will be transformative for a vast range of problems throughout biology and chemistry 1/n
These are already being used today to design new drugs. And everyday they get much better. They work by predicting the solution of the Schrödinger equation much faster than it’s possible to directly solve it.
They predict the forces on atoms allowing us to simulate how atoms and molecules move. They therefore connect the quantum scale to the classical scale. But as important an achievement as that is they are even more useful than that.
It should be possible to automate this process as we know from renormalisation group theory that there are recurring mathematical features involved in connecting scales.
In particular at each scale there is the problem of ignoring the fast dynamics that can be ignored or approximated with Gaussian noise and keeping track of the important features that are useful for prediction. Machine learning is the perfect tool for this.
Neural network potentials are already enabling this. (Diffusion models and Alphafold can also be interpreted as more general examples of neural network potentials) We should soon be able to accurately simulate the intermediate scale processes smaller than we can observe directly.