Related papers: Yau-YauAL: A computer tool for solving nonlinear f…
Nonlinear filter has long been an important problem in practical industrial applications. The Yau-Yau method is a highly versatile framework that transforms nonlinear filtering problems into initial-value problems governed by the Forward…
At the beginning of this century, a real time solution of the nonlinear filtering problem without memory was proposed in [1, 2] by the third author and his collaborator, and it is later on referred to as Yau-Yau algorithm. During the last…
Nonlinear state estimation under noisy observations is rapidly intractable as system dimension increases. We introduce an improved Yau-Yau filtering framework that breaks the curse of dimensionality and extends real-time nonlinear filtering…
Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of…
This paper presents a systematic review of recent advances in nonlinear filtering algorithms, structured into three principal categories: Kalman-type methods, Monte Carlo methods, and the Yau-Yau algorithm. For each category, we provide a…
We introduce Yao, an extensible, efficient open-source framework for quantum algorithm design. Yao features generic and differentiable programming of quantum circuits. It achieves state-of-the-art performance in simulating small to…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…
The Jaya R package offers a robust and versatile implementation of the parameter-free Jaya optimization algorithm, suitable for solving both single-objective and multi-objective optimization problems. By integrating advanced features such…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
The importance of computers is continually increasing in radiotherapy. Efficient algorithms, implementations and the ability to leverage advancements in computer science are crucial to improve cancer care even further and deliver the best…
The goal of this article is twofold. Firstly, nonlinear system identification is introduced to a wide audience, guiding practicing engineers and newcomers in the field to a sound solution of their data driven modeling problems for nonlinear…
Like many groups considering the new programming language Julia, we faced the challenge of accessing the algorithms that we develop in Julia from R. Therefore, we developed the R package JuliaConnectoR, available from the CRAN repository…
We present QuantumToolbox$.$jl, an open-source Julia package for simulating open quantum systems. Designed with a syntax familiar to users of QuTiP (Quantum Toolbox in Python), it harnesses Julia's high-performance ecosystem to deliver fast…
We present FractionalDiffEq.jl, a comprehensive solver suite for solving fractional differential equations, featuring high-performance numerical algorithms in the Julia programming language. FractionalDiffEq.jl is designed to be…
Simulation of non-adiabatic dynamics of a quantum system coupled to dissipative environments poses significant challenges. New sophisticated methods are regularly being developed with an eye towards moving to larger systems and more…
We present NEP-PACK a novel open-source library for the solution of nonlinear eigenvalue problems (NEPs). The package provides a framework to represent NEPs, as well as efficient implementations of many state-of-the-art algorithms. The…
Numerical investigations are an important research tool in quantum information theory. There already exists a wide range of computational tools for quantum information theory implemented in various programming languages. However, there is…
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…