I wonder, if there is a way to approach the DFT problem in an inverse manner
For example, instead of trying to optimise the energy and geometry of a molecule, we instead take a table of molecules with known and accurate experimental values, and then fit a guess functional in it, and optimise that functional instead
Then said functional optimised from machine learning can then become a custom functional to calculate other molecules with
hmmm I am not sure, I might read them in more detail to be sure. Perhaps optimising the functional parameters is sufficient to define the functional. I initially though to define a functional you need to do something a lot more than just specifying a few paramters
That approach will in any case only result in a functional that reproduces results based on experimental data. So it really is just (semi-)empirical. Why would you need DFT in the first place then? You can get such results a lot faster without it. DFT is in theory exact, and it is the goal to minimise the guessing within the functional. We would like to have a method that is right (or even wrong) for the right reasons.
Not a functional to be right, but only on occasion, because it relies on inconsistent error cancelation.
IIRC Burke is using machine learning to make new functionals - but when you go that route you have to consider that you will never understand what the functional actually does. And if you have understanding as a fundamental scientific principle, that's probably not the most clever way to do things.
I recently read the qchem manual which mentioned that there are no known algorithms to derive functionals that can approximate the exact limit, which is why it makes me curious of this question, as mathematically speaking it will be trying to solve for the functional that satisfy the schrodinger equation
This is in contrast to the ab initio methods where the more determinants, higher order perturbation terms etc. were added, the closer we can achieve the exact limit
> While more accurate forms of such functionals are constantly being developed, there is no systematic way to improve the functional to achieve an arbitrary level of accuracy. Thus, the traditional approaches offer the possibility of achieving a systematically-improvable level of accuracy, but can be computationally demanding, whereas DFT approaches offer a practical route, but the theory is currently incomplete.
You can't just say "add machine learning" and magically get a solution: you need to work out what parameters and functions you're trying to use to get closer to the real solution.
As a simple example: you can take a test set of molecules and optimise the percentage of HF exchange contribution to fit best to the test set's energies calculated at a higher level of theory.
But if you don't have a good set of parameters to vary, you're not going to get anything sensible out of fitting.
(And neural-net-type machine-learning is basically layers and layers of regression fitting AIUI.)
Oh, and the B3LYP functional is made that way as well: I think the Becke exchange part has 3 parameters (hence B3) that are optimised over a set of molecules.
Wait, wait, you actually thought nuclear decay is in any way related with how nucleus moves alongside with atom? This idea is so weird I didn't got what you were saying... — Mithoron52 mins ago
@Mithoron I think you can probably take a nicer tone than that.
@Zhe Hmm, I checked out and you have lots of comments, but surprisingly small amount of votes/flags/edits You could easily have 4 golden badges or more with similar level of activity.
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The Periodic Table
The Periodic Table