相关论文: Projected site-occupation embedding theory

We propose the application of occupation measure theory to the classical problem of transient stability analysis for power systems. This enables the computation of certified inner and outer approximations for the region of attraction of a…

The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…

Optimal transport (OT), and in particular the Wasserstein distance, has seen a surge of interest and applications in machine learning. However, empirical approximation under Wasserstein distances suffers from a severe curse of…

This paper contributes a new State Of The Art (SOTA) for Semantic Textual Similarity (STS). We compare and combine a number of recently proposed sentence embedding methods for STS, and propose a novel and simple ensemble knowledge…

Accurate and reliable algorithms to solve complex impurity problems are instrumental to a routine use of quantum embedding methods for material discovery. In this context, we employ an efficient selected configuration interaction impurity…

Quantum embedding schemes have the potential to significantly reduce the computational cost of first principles calculations, whilst maintaining accuracy, particularly for calculations of electronic excitations in complex systems. In this…

The Hubbard model provides a test bed to investigate the complex behaviour arising from electron-electron interaction in strongly-correlated systems and naturally emerges as the foundation model for lattice density functional theory (DFT).…

We introduce a spectral embedding algorithm for finding proximal relationships between nodes in signed graphs, where edges can take either positive or negative weights. Adopting a physical perspective, we construct a Hamiltonian which is…

Most realistic calculations of moderately correlated materials begin with a ground-state density functional theory (DFT) calculation. While Kohn-Sham DFT is used in about 40,000 scientific papers each year, the fundamental underpinnings are…

The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD), which is a template-free method that represents the combination of different intrinsic modes on a time-frequency map (i.e., the Hilbert spectrum). The…

The dynamical mean-field theory (DMFT) is employed to study the Mott transition in the semi-infinite Hubbard model at half-filling and zero temperature. We consider the low-index surfaces of the three-dimensional simple-cubic lattice and…

In the last few years, large improvements in image clustering have been driven by the recent advances in deep learning. However, due to the architectural complexity of deep neural networks, there is no mathematical theory that explains the…

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…

The structural phase transitions and computational complexity of random 3-SAT instances are traditionally described using thermodynamic analogies from statistical physics, such as Replica Symmetry Breaking and energy landscapes. While…

The 2D half-filled Hubbard model is studied by a nonperturbative analytic theory of correlator projection. The original dynamical mean-field approximation (DMFA) is reproduced at the first-order projection and then improved by systematic…

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here…

Ensemble density functional theory (EDFT) is a promising alternative to time-dependent density functional theory for computing electronic excitation energies. Using coordinate scaling, we prove several fundamental exact conditions in EDFT…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

Motivated by recent progress in the realization of artificial gauge fields and $SU(N)$ Mott insulators using alkaline-earth-like atoms in optical lattices, we develop an unbiased $SU(N)$ real-space dynamical mean-field theory (DMFT)…

We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation between the site…