Related papers: Prospects of tensor-based numerical modeling of th…
In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…
As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
Latent class models are powerful statistical modeling tools widely used in psychological, behavioral, and social sciences. In the modern era of data science, researchers often have access to response data collected from large-scale surveys…
In this paper, we define a scalar complex potential $\mathcal{S}$ for an arbitrary electromagnetic field. This potential is a modification of the two scalar potential functions introduced by E. T. Whittaker. By use of a complexified…
Total energies of crystal structures can be calculated to high precision using quantum-based density functional theory (DFT) methods, but the calculations can be time consuming and scale badly with system size. Cluster expansions of total…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order $n$ can…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with respect the lattice sites is considered as the basic variable of the many-body problem. A…
Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…
Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful…
We present an analytical many-body formalism for systems of spherical particles carrying arbitrary free charge distributions and interacting in a polarizable electrolyte solution, that we model within the linearized Poisson--Boltzmann…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
This paper gives a systematic method for constructing an N-body potential, approximating the true potential, that accurately captures meso-scale behavior of the chemical or biological system using pairwise potentials coming from…
Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into…
The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…