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Data-driven discovery of governing equations from time-series data provides a powerful framework for understanding complex biological systems. Library-based approaches that use sparse regression over candidate functions have shown…
Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to…
Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…
We might hope that when faced with unexpected inputs, well-designed software systems would fire off warnings. Machine learning (ML) systems, however, which depend strongly on properties of their inputs (e.g. the i.i.d. assumption), tend to…
We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We…
We demonstrate that the machine learning of density functionals allows one to determine simultaneously the equilibrium chemical potential across simulation datasets of inhomogeneous classical fluids. Minimization of a loss function based on…
Machine learning (ML) enables the development of interatomic potentials that promise the accuracy of first principles methods while retaining the low cost and parallel efficiency of empirical potentials. While ML potentials traditionally…
Due to efficient scaling with electron number N, density functional theory (DFT) is widely used for studies of large molecules and solids. Restriction of an exact mean-field theory to local potential functions has recently been questioned.…
The excess free energy functional of classical density functional theory depends upon the type of fluid model, specifically on the choice of (pair) potential, is unknown in general, and is approximated reliably only in special cases. We…
Density functional theory offers a very accurate way of computing materials properties from first principles. However, it is too expensive for modelling large-scale molecular systems whose properties are, in contrast, computed using…
Density Functional Theory has long struggled to obtain the exact exchange-correlational (XC) functional. Numerous approximations have been designed with the hope of achieving chemical accuracy. However, designing a functional involves…
Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the…
With the recent rapid progress in the machine-learning (ML), there have emerged a new approach using the ML methods to the exchange-correlation functional of density functional theory. In this chapter, we review how the ML tools are used…
Electron density is a fundamental quantity, which can in principle determine all ground state electronic properties of a given system. Although machine learning (ML) models for electron density based on either an atom-centered basis or a…
The exact universal functional of integer charge leads to an extension to fractional charge asymptotically when it is applied to a system made of asymptotically separated densities. The extended functional is asymptotically local and is…
The enormous structural and chemical diversity of metal-organic frameworks (MOFs) forces researchers to actively use simulation techniques on an equal footing with experiments. MOFs are widely known for outstanding adsorption properties, so…
Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically…
We use machine learning methods to approximate a classical density functional. As a study case, we choose the model problem of a Lennard Jones fluid in one dimension where there is no exact solution available and training data sets must be…
We present a novel deep learning (DL) approach to produce highly accurate predictions of macroscopic physical properties of solid solution binary alloys and magnetic systems. The major idea is to make use of the correlations between…
While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…