Related papers: Time-Dependent Duhamel Renormalization method with…
This article deals with time-fractional diffusion equations with time-dependent singular source term. Whenever the order of the time-fractional derivative is either multi-term, distributed or space-dependent, we prove that the system admits…
With the rapid development of machine learning applications on time-series data, accurately assessing the value of training samples has become essential for data selection, noise detection, and model optimization. However, traditional data…
The Time Dependent Boltzmann equation (TDBE) is a viable option to study strongly out-of-equilibrium thermalization dynamics which are becoming increasingly critical for many novel physical applications like Ultrafast thermalization,…
We show that the time-dependent Schr\"odinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of…
Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe…
We present a unified framework for the rigorous derivation of conservation laws and related identities for nonlinear Schr\"odinger equations with power-type nonlinearities. This approach treats the equation in its Duhamel form and uses the…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
Discrete Token Modeling (DTM), which employs vector quantization techniques, has demonstrated remarkable success in modeling non-natural language modalities, particularly in time series generation. While our prior work SDformer established…
Existing image deraining methods typically rely on single-input, single-output, and single-scale architectures, which overlook the joint multi-scale information between external and internal features. Furthermore, single-domain…
Time series forecasting is crucial for various applications, such as weather, traffic, electricity, and energy predictions. Currently, common time series forecasting methods are based on Transformers. However, existing approaches primarily…
In this work we present a derivation of the real-time time-dependent orbital-optimized M{\o}ller-Plesser TDOMP2 and its biorthogonal companion, time-dependent non-orthogonal OMP2 (TDNOMP2), theory starting from the time-dependent…
Time dependent density matrix renormalization group (TD-DMRG) has become one of the cutting edge methods of quantum dynamics for complex systems. In this paper, we comparatively study the accuracy of three time evolution schemes in TD-DMRG,…
We propose a novel approach to simulate the solution of the time-dependent Schr\"odinger equation with a general variable potential. The key idea is to approximate the Titchmarsh-Weyl m-function (exact Dirichlet-to-Neumann operator) by a…
The variational calculation of the two-electron reduced density matrix (2-RDM) is extended to periodic molecular systems. If the 2-RDM theory is extended to the periodic case without consideration of time-reversal symmetry, however, it can…
We propose a finite-difference algorithm for solving the time-dependent Ginzburg-Landau (TDGL) equation coupled to the appropriate Maxwell equation. The time derivatives are discretized using a second order semi-implicit scheme which, for…
This paper is concerned with the approximation of linear and nonlinearinitial-boundary-value problems of pseudo-parabolic equations with Dirichlet boundary conditions. They are discretized in space by spectral Galerkin and collocation…
This paper extends our earlier approach [cf. Phys. Plasmas 17, 032503 (2010), 23, 022308 (2016)] to obtaining a priori bounds on enstrophy in neutral fluids (R-Euler) and ideal magnetohydrodynamics (R-MHD). This results in a far-reaching…
Value functions arise as a component of algorithms as well as performance metrics in statistics and engineering applications. Computation of the associated Bellman equations is numerically challenging in all but a few special cases. A…
An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a…
This work outlines a time-domain numerical integration technique for linear hyperbolic partial differential equations sourced by distributions (Dirac $\delta$-functions and their derivatives). Such problems arise when studying binary black…