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The embedded topic model (ETM) is a widely used approach that assumes the sampled document-topic distribution conforms to the logistic normal distribution for easier optimization. However, this assumption oversimplifies the real…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
Diffusion models are state-of-the-art generative models, yet their samples often fail to satisfy application objectives such as safety constraints or domain-specific validity. Existing techniques for alignment require gradients, internal…
Training diffusion models is always a computation-intensive task. In this paper, we introduce a novel speed-up method for diffusion model training, called, which is based on a closer look at time steps. Our key findings are: i) Time steps…
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
In this paper we consider an approach to improve the performance of exponential Runge--Kutta integrators and Lawson schemes} in cases where the solution of a related, but usually much simpler, problem can be computed efficiently. While for…
We consider the distributed optimization problem where $n$ agents each possessing a local cost function, collaboratively minimize the average of the $n$ cost functions over a connected network. Assuming stochastic gradient information is…
A collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness…
The paper is focused on the numerical solution of stochastic reaction-diffusion problems. A special attention is addressed to the conservation of mean-square dissipativity in the time integration of the spatially discretized problem,…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…
In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard…
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile…
The tempered fractional diffusion equation could be recognized as the generalization of the classic fractional diffusion equation that the truncation effects are included in the bounded domains. This paper focuses on designing the high…
Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…
This article provides techniques of raising the regularity of fractional order equations and resolves fundamental questions on the one-dimensional homogeneous boundary-value problem of skewed (double-sided) fractional diffusion advection…
In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
In this paper, we focus on the finite difference approximation of nonlinear degenerate parabolic equations, a special class of parabolic equations where the viscous term vanishes in certain regions. This vanishing gives rise to additional…