Related papers: Dynamic Learning of Correlation Potentials for a T…
We calculate the `exact' potential corresponding to a one-dimensional interacting system of two electrons with a specific, tailored density. We use one-dimensional density-functional theory with a local-density approximation (LDA) on the…
Over the years, several schemes have been proposed to describe multireference systems with Kohn-Sham Density Functional Theory. Problematic is the combination of two aspects: the Kohn-Sham reference wavefunction is usually taken to be a…
Including prior knowledge is important for effective machine learning models in physics, and is usually achieved by explicitly adding loss terms or constraints on model architectures. Prior knowledge embedded in the physics computation…
Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the…
We introduce a new class of exchange-correlation potentials for a static and time-dependent Density Functional Theory of strongly correlated systems in 3D. The potentials are obtained via Dynamical Mean Field Theory and, for strong enough…
Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…
This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…
A long-standing puzzle in density-functional theory is the issue of the long-range behavior of the Kohn-Sham exchange-correlation potential at metal surfaces. As an important step towards its solution, it is proved here, through a rigurouos…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
Reproducing Kernel Hilbert Space (RKHS) is the common mathematical platform for various kernel methods in machine learning. The purpose of kernel learning is to learn an appropriate RKHS according to different machine learning scenarios and…
Correlation-driven phenomena in molecular periodic systems are challenging to predict computationally not only because such systems are periodically infinite but also because they are typically strongly correlated. Here we generalize the…
We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centred auxiliary basis, which enables an accurate expansion of the all-electron density in…
A fundamental weakness of density functional theory (DFT) is the difficulty in making systematic improvements to approximations for the exchange and correlation functionals. In this paper, we follow a wave-function-based approach [N.I.…
Machine-learning interatomic potentials (MLIPs) have enabled molecular dynamics at near ab initio accuracy, yet remain limited to energies and forces by construction, leaving electronic observables such as dipole moments and…
Predictivity of the Kohn-Sham approach to dynamical problems, when regarded as an initial value problem in a time-dependent density functional framework, is analysed for a class of models for which the argument devised in the work of Maitra…
An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…
The correlation energy in density functional theory can be expressed exactly in terms of the change in the probability of finding two electrons at a given distance $r_{12}$ (intracule density) when the electron-electron interaction is…
We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…
Many dynamical systems exhibit similar structure, as often captured by hand-designed simplified models that can be used for analysis and control. We develop a method for learning to correspond pairs of dynamical systems via a learned latent…