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Power systems are undergoing unprecedented transformations with the incorporation of larger amounts of renewable energy sources, distributed generation and demand response. All these changes, while potentially making power grids more…
The average energy curvature as a function of the particle number is a molecule-specific quantity, which measures the deviation of a given functional from the exact conditions of density functional theory (DFT). Related to the lack of…
In a large class of factorizing scattering models, we construct candidates for the local energy density on the one-particle level starting from first principles, namely from the abstract properties of the energy density. We find that the…
We consider the graph dynamical systems known as k-reversible processes. In such processes, each vertex in the graph has one of two possible states at each discrete time step. Each vertex changes its state between the current time and the…
Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic…
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…
The quantum theory of atoms in molecules (QTAIM) gives access to well-defined local atomic energies. Due to their locality, these energies are potentially interesting in fitting atomistic machine learning models as they inform about…
Density Functional Theory's Kohn-Sham (KS) potential emerges as the minimizing effective potential in an unconstrained variational scheme that does not involve fixing the unknown single-electron density. The physical content behind the…
This paper proves a new general K-network constrained energy reliability global factorization theorem. As in the unconstrained case, beside its theoretical mathematical importance the theorem shows how to do parallel processing in exact…
Neural Gas (NG) constitutes a very robust clustering algorithm given euclidian data which does not suffer from the problem of local minima like simple vector quantization, or topological restrictions like the self-organizing map. Based on…
We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and potential. This functional is extremely non-local, but…
The optimization of neural wave functions in variational Monte Carlo crucially relies on a robust convergence criterion. While the energy variance is theoretically a definitive measure, its practical application as a primary convergence…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
Vacuum energy in quantum field theory, being the sum of zero-point energies of all field modes, is formally infinite but yet, after regularization or renormalization, can give rise to finite observable effects. One way of understanding how…
In machine learning energy potentials for atomic systems, forces are commonly obtained as the negative derivative of the energy function with respect to atomic positions. To quantify aleatoric uncertainty in the predicted energies, a widely…
We discuss the property of a.e. and in mean convergence of the Kohonen algorithm considered as a stochastic process. The various conditions ensuring the a.e. convergence are described and the connection with the rate decay of the learning…
An accurate expression of the kinetic energy density of an electronic distribution in terms of the single particle reduced density matrix for atomic and molecular systems is a long-standing problem in electron structure theory. Existing…
We demonstrate a convolutional neural network trained to reproduce the Kohn-Sham kinetic energy of hydrocarbons from electron density. The output of the network is used as a non-local correction to the conventional local and semi-local…
The traditional framework of quantum metrology commonly assumes unlimited access to resources, overlooking resource constraints in realistic scenarios. As such, the optimal strategies therein can be infeasible in practice. Here, we…
We show that the intelligence of the machine-learning potential arises from its ability to infer the reference atomic-energy function from a given set of total energies. By utilizing invariant points in the feature space at which the atomic…