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Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…

Computer Vision and Pattern Recognition · Computer Science 2017-12-18 Risheng Liu , Xin Fan , Shichao Cheng , Xiangyu Wang , Zhongxuan Luo

In the course of basic physics, more precisely the course of classical mechanics should be understood as clearly as possible the subject of rotational dynamics for students of science and engineering, to have clarity with the issues…

Physics Education · Physics 2018-12-12 Alex Estupiñán , Miguel Pico , Raul Ortiz

Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…

High Energy Physics - Theory · Physics 2007-05-23 Daniela Bigatti

To enhance the undergraduate and graduate engineering education for nanoscale materials, devices and systems, we report a multi-disciplinary course based on the integration of theory, hands-on laboratory and hands-on computation into a…

Mesoscale and Nanoscale Physics · Physics 2013-03-27 Hassan Raza , Tehseen Z. Raza

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

Machine Learning · Computer Science 2025-07-17 Zachary James , Joseph Guinness

GNNs are a paradigm-shifting neural architecture to facilitate the learning of complex multi-agent behaviors. Recent work has demonstrated remarkable performance in tasks such as flocking, multi-agent path planning and cooperative coverage.…

Robotics · Computer Science 2022-03-02 Jan Blumenkamp , Steven Morad , Jennifer Gielis , Qingbiao Li , Amanda Prorok

This text is the support for the course of Modeling of Solids, of the Master of Mechanics of the University Paris-Saclay - Curriculum MMM: Mathematical Methods for Mechanics, held at Versailles. The course is the continuation of the course…

Classical Physics · Physics 2026-02-24 Paolo Vannucci

For certain dynamical systems it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system close to a non-hyperbolic…

Dynamical Systems · Mathematics 2020-09-22 Bernard Haasdonk , Boumediene Hamzi , Gabriele Santin , Dominik Wittwar

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

Statistics Theory · Mathematics 2025-12-16 D. Andrew Brown , Peter Kiessler , John Nicholson

In this work, we propose a geometric framework for analyzing mechanical manipulation, for instance, by a robotic agent. Under the assumption of conservative forces and quasi-static manipulation, we use energy methods to derive a metric. In…

Optimization and Control · Mathematics 2024-02-27 Domenico Campolo , Franco Cardin

This paper presents a proposed alternative to simulate non-linear dynamical systems. This has an application in bachelor programs like: Electrical and mechanical engineering, Networks and Telecommunications engineering, Mechanical…

Systems and Control · Electrical Eng. & Systems 2019-09-04 Felipe de Jesús Torres , Monserrat Sugey Arredondo , José Manuel Martinez , Víctor Manuel Ocampo

We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…

Mathematical Physics · Physics 2007-05-23 J. F. Colombeau

We have designed, built and operated a physical pendulum which allows one to demonstrate experimentally the behaviour of the pendulum under any equation of motion for such a device for any initial conditions. All parameters in the equation…

Popular Physics · Physics 2015-05-13 H. Hauptfleisch , T. Gasenzer , K. Meier , O. Nachtmann , J. Schemmel

Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our…

Machine Learning · Computer Science 2020-09-15 Alvaro Sanchez-Gonzalez , Jonathan Godwin , Tobias Pfaff , Rex Ying , Jure Leskovec , Peter W. Battaglia

The prepared doctoral dissertation focuses on studying dynamics of systems composed of magnetic pendulums subjected to a non-stationary magnetic field. A magnetic pendulum is a physical pendulum with a magnet attached to its end and is…

Pattern Formation and Solitons · Physics 2024-01-22 Krystian Polczyński

Dynamics is a core discipline in Mechanical and Aerospace Engineering programs and with the ubiquitous nature of control in modern day applications, the field of mechatronics has gained popularity. Mechatronics refers to the field of…

Physics Education · Physics 2023-03-06 Adrian Stein , Tarik Parcic , Tarunraj Singh

This paper describes a system capable of semi-automatically filling an XML template from free texts in the clinical domain (practice guidelines). The XML template includes semantic information not explicitly encoded in the text (pairs of…

Artificial Intelligence · Computer Science 2007-06-11 Amanda Bouffier , Thierry Poibeau

Micro-scale mechanisms, such as inter-particle and particle-fluid interactions, govern the behaviour of granular systems. While particle-scale simulations provide detailed insights into these interactions, their computational cost is often…

Numerical simulation is an essential tool in many areas of science and engineering, but its performance often limits application in practice or when used to explore large parameter spaces. On the other hand, surrogate deep learning models,…

Machine Learning · Computer Science 2022-05-18 Mario Lino , Stati Fotiadis , Anil A. Bharath , Chris Cantwell

The control of granular materials, showing up in many industrial applications, is a challenging open research problem. Granular material systems are complex-behavior (as they could have solid-, fluid-, and gas-like behaviors) and…

Optimization and Control · Mathematics 2023-02-08 Yuichiro Aoyama , Amin Haeri , Evangelos A. Theodorou