Related papers: Tensor Network Lattice Boltzmann Method for Data-C…
A general derivation is proposed for several boundary conditions arisen in the lattice Boltzmann simulations of various physical problems. Pair-wise moment conservations are proposed to enforce the boundary conditions with given macroscopic…
Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier-Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena…
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding…
The pseudopotential lattice Boltzmann method (LBM) is a prominent approach for simulating multiphase flows, valued for its physical intuitiveness and computational tractability. However, existing immiscible pseudopotential methods for…
Simulating fluid-granular flows is crucial for understanding natural disasters, industrial processes, and visually realistic phenomena in computer graphics. These systems are challenging to simulate because of the strong nonlinear coupling…
We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design…
Matrix Product State (MPS) is a versatile tensor network representation widely applied in quantum physics, quantum chemistry, and machine learning, etc. MPS sampling serves as a critical fundamental operation in these fields. As the…
In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint…
A recently introduced family of lattice Boltzmann (LB) models (Karlin, B\"osch, Chikatamarla, Phys. Rev. E, 2014) is studied in detail for incompressible two-dimensional flows. A framework for developing LB models based on entropy…
Integrating machine learning techniques in established numerical solvers represents a modern approach to enhancing computational fluid dynamics simulations. Within the lattice Boltzmann method (LBM), the collision operator serves as an…
Physics-Informed Neural Networks (PINNs) have demonstrated considerable success in solving complex fluid dynamics problems. However, their performance often deteriorates in regimes characterized by steep gradients, intricate boundary…
Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…
A D2Q9 Hybrid Lattice Boltzmann Method (HLBM) is proposed for the simulation of both compressible subsonic and supersonic flows. This HLBM is an extension of the model of Feng et al: [12], which has been found, via different test cases, to…
We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. This model is based on a 16-discrete-velocity model. The collision step is first calculated in the moment space and…
Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the…
In this paper, we propose a computational framework,which is based on a domain decomposition technique, to employ both finite element method (which is a popular continuum modeling approach) and lattice Boltzmann method (which is a popular…
We propose an accelerated computational fluid dynamics framework based on a hybrid Fourier Neural Operator-Lattice Boltzmann Method (FNO-LBM) for steady and unsteady weakly compressible flows. FNO-based initialization significantly…
Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on…