into Machine-Learned Physics
Authors: Li Li et al Code: https://github.com/google-research/google-research/tree/master/jax_dft Is-Survey: No Library: Jax Model: Global Convolution URL: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.126.036401 https://journals.aps.org/prl/supplemental/10.1103/PhysRevLett.126.036401/supp.pdf Year: 2020
For XC, recent works focus on learning the XC potential (not functional) from inverse KS [31] and use it in the KS-DFT scheme [32–35]. An important step forward was made last year, when it was shown that a neural network could find functionals using only three molecules by training on both energies and densities [36] [[Completing-dft-by-ml]], obtaining accuracy comparable to human-designed functionals and generalizing to yield accurate atomization energies of 148 small molecules [37]. But this pioneering work does not yield chemical accuracy or approximations that work in the dissociation limit. Moreover, it uses gradient-free optimization which usually suffers from poor convergence behavior on the large number of parameters used in modern neural networks [38–40].
In other ML work, functionals are trained on either energies alone [41–44], or even densities [33,34 [Toward-the-Exact-Exchange–Correlation-Potential],45], but only after convergence. By incorporating the KS equations into the training, thereby learning the relation between density and energy at every iteration, we find accurate models with very little data and much greater generalizability.
Unlike previous works [33, 34 [Toward-the-Exact-Exchange–Correlation-Potential], 35 [Neural-network-Kohn-Sham-exchange-correlation-potetial] ] that explicitly included the KS or XC potential in the loss function, our model never uses the exact KS potential. In our KSR setup, the model aims to predict ϵXC, from which the derived vs yields accurate density. Therefore, predicting vXC is a side product. We also address some concerns on training explicitly with vXC. One artifact is that generating the exact vs requires an additional inverse calculation, which is known to be numerically unstable [31]. Schmidt et al. [33] observe outliers while generating training vXC from inverse KS. While vXC is a fascinating and useful object for theoretical study because its relation to the density is extremely delicate, it is far more practical to simply use the density to train on [36] [[Completing-dft-by-ml]].