I'm a student and now studying quantum chemistry but also interested in machine learning (ML) and materials informatics (MI).
In order to understand an ML method for MI, I tried to use the smooth overlap of atomic positions (SOAP), which is a widely-used descriptor for molecules. Using the SOAP descriptor as the input, I implemented a simple neural network (NN) model in PyTorch (see Fig.1 (a)). After training the NN model with the energy, the accuracy was very good, and then I transferred the trained NN model to the HOMO-LUMO gap. I obtained the results as Fig.1 (b) and (c).
Fig.1: (a) The SOAP descriptor input-based NN model. (b) Learning curve for the atomization energy (eV) provided by the QM9 database, which is a famous benchmark database in MI. Test error of energy is about 2.0 eV. (c) Transfer learning for the HOMO-LUMO gap with the pre-trained model.
I found that the transfer result was very poor (the random and pre-trained accuracies (errors) are the same, about 1.2 eV as shown in Fig.1 (c))... For my study, I tried to use other ML models (e.g., graph neural network and neural network potential), but the results were also very poor or much worse...
Here, I have a question; does this mean that the above NN model just fitted to only the energy, did not learn physics at all? In addition, do most of the ML models that just fit only the energy make sense from the view point of DFT? In DFT, as far as I have studied, solving the Kohn-Sham equation yields the ground state energy and density by variational principle, and also provides the eigenvalues (i.e., orbital energies), so we can know various physical properties such as the HOMO and LUMO.
My impression is that ML models just predict "similar molecules have similar energies (see Fig.2)", and it is very easy if we have a large number of similar molecules and their energies in the database. However, even in this case, can we say that "ML can approximate the DFT calculation"? (In fact, most of the research papers in ML and MI claim so, and I'm honestly very confused…)
Fig.2: The energy of the right-side molecule must be close to about -86.7X eV (the actual energy is -86.75 eV), but this is very easy to predict because we already know the energies of the left-side molecules as the training data samples, which are very similar to the right-side molecule.
Postscript: actually, I'm now interested in the "foundation model" in AI/ML research (https://arxiv.org/pdf/2108.07258.pdf). I would like to know whether AI/ML can solve various tasks (e.g., not only predict the total energy but also provide the HOMO LUMO eigenvalues, density, and other physical properties) with one (pre-trained) model. I would like to ask about the possibility as another question.