相关论文: A Sampling-Based Adaptive Rank Approach to the Wig…
We construct a finite element discretization and time-stepping scheme for the incompressible Euler equations with variable density that exactly preserves total mass, total squared density, total energy, and pointwise incompressibility. The…
Enhanced sampling methods such as metadynamics and umbrella sampling have become essential tools for exploring the configuration space of molecules and materials. At the same time, they have long faced a number of issues such as the…
A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
We study the low-energy solutions to the 3D compressible Navier-Stokes-Poisson equations. We first obtain the existence of smooth solutions with small $L^2$-norm and essentially bounded densities. No smallness assumption is imposed on the…
Understanding the system-level spectral immittance response of capacitive energy storage devices with analytically tractable physics-based models is not only important for the progress of the technology, but also allows to develop new…
We study the global strong solutions to the compressible Navier-Stokes system with potential temperature transport in $\mathbb{R}^n.$ Different from the Navier-Stokes-Fourier system, the pressure is a nonlinear function of the density and…
Low rank recovery problems have been a subject of intense study in recent years. While the rank function is useful for regularization it is difficult to optimize due to its non-convexity and discontinuity. The standard remedy for this is to…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
Achieving self-consistent convergence with the conventional effective-mass approach at ultra-low temperatures (below $4.2~K$) is a challenging task, which mostly lies in the discontinuities in material properties (e.g., effective-mass,…
Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is…
In panel data subject to nonignorable attrition, auxiliary (refreshment) sampling may restore full identification under weak assumptions on the attrition process. Despite their generality, these identification strategies have seen limited…
The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three-dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute…
Energy evaluation using fast Fourier transforms enables sampling billions of putative complex structures and hence revolutionized rigid protein-protein docking. However, in current methods efficient acceleration is achieved only in either…
In this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits. The approximation is achieved through iterative compression of the density matrix based on…
The computational cost of stiff chemical kinetics remains a dominant bottleneck in reacting-flow simulation, yet hybrid integration strategies are typically driven by hand-tuned heuristics or supervised predictors that make myopic decisions…
Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…