Related papers: PIETOOLS 2025: User Manual
Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…
Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with…
Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…
This document presents 30 different privacy guidelines that can be used to both design and assess IoT applications and IoT middleware platforms. These guidelines can be broadly categorised into eight categories, namely, MINIMIZE ( ), HIDE (…
"Model-free control" and the corresponding "intelligent" PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into…
The simulation and parameter optimization of coupled ocean circulation and ecosystem models in three space dimensions is one of the most challenging tasks in numerical climate research. Here we present a scientific toolkit that aims at…
Background: Mathematical models based on ordinary differential equations (ODEs) are essential tools across various scientific disciplines, including biology, ecology, and healthcare informatics. They are used to simulate complex dynamic…
Document processing automation remains a critical challenge in enterprise environments, where traditional manual approaches are labor-intensive and error-prone. We present MADP, a multi-agent architecture that addresses the challenge of…
Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world's largest supercomputers. One…
As the field of data science continues to grow, there will be an ever-increasing demand for tools that make machine learning accessible to non-experts. In this paper, we introduce the concept of tree-based pipeline optimization for…
In 2020, DIDO$^\copyright$ turned 20! The software package emerged in 2001 as a basic, user-friendly MATLAB$^\circledR$ teaching-tool to illustrate the various nuances of Pontryagin's Principle but quickly rose to prominence in 2007 after…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
This study presents a comprehensive overview of PIML techniques in the context of condition monitoring. The central concept driving PIML is the incorporation of known physical laws and constraints into machine learning algorithms, enabling…
We present Paicos, a new object-oriented Python package for analyzing simulations performed with Arepo. Paicos strives to reduce the learning curve for students and researchers getting started with Arepo simulations. As such, Paicos…
This paper discusses the algorithms and implementations of three Mathematica packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs. The first package, PainleveTest.m, symbolically…
We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…
Unmanned Aerial Vehicles (UAVs) have gained widespread recognition for their diverse applications, ranging from surveillance to delivery services. Among the various control algorithms employed to stabilize and navigate UAVs, the…
Impulse-to-peak response (I2P) analysis for state-space ordinary differential equation (ODE) systems is a well-studied classical problem. However, the techniques employed for I2P optimal control of ODEs have not been extended to partial…
IFISS is an established MATLAB finite element software package for studying strategies for solving partial differential equations (PDEs). IFISS3D is a new add-on toolbox that extends IFISS capabilities for elliptic PDEs from two to three…
In recent years, a wide variety of automated machine learning (AutoML) methods have been proposed to search and generate end-to-end learning pipelines. While these techniques facilitate the creation of models for real-world applications,…