Related papers: Pseudospectral method for solving PDEs using Matri…

Spectral methods employing non-standard polynomial bases, such as M\"untz polynomials, have proven effective for accurately solving problems with solutions exhibiting low regularity, notably including sub-diffusion equations. However, due…

This study introduces the Homotopy Perturbation Sumudu Transform Method (HPSTM), a novel hybrid approach combining the Sumudu transform with homotopy perturbation to solve nonlinear fractional partial differential equations (FPDEs),…

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…

Quantum mechanical calculations for material modelling using Kohn-Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for $N$ smallest eigenvector-eigenvalue pairs with $N$ proportional to the number…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…

A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert…

By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…

Hidden Markov models (HMMs) are widely used statistical models for modeling sequential data. The parameter estimation for HMMs from time series data is an important learning problem. The predominant methods for parameter estimation are…

We present a method for solving implicit (factored) Markov decision processes (MDPs) with very large state spaces. We introduce a property of state space partitions which we call epsilon-homogeneity. Intuitively, an epsilon-homogeneous…

Neural network solvers represent an innovative and promising approach for tackling time-fractional partial differential equations by utilizing deep learning techniques. L1 interpolation approximation serves as the standard method for…

Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…

Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…

Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…

This paper presents a new approach on stretch processing for a fine range estimation using MPM (Matrix Pencil Method). The conventional method utilizes FFT (Fast Fourier Transform) with limited range resolution with its fixed number of…

We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…

Partially-Observable Markov Decision Processes (POMDPs) are typically solved by finding an approximate global solution to a corresponding belief-MDP. In this paper, we offer a new planning algorithm for POMDPs with continuous state, action…

In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…