Related papers: pynamicalsys: A Python toolkit for the analysis of…
Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…
In this work, we present our generic framework to construct, simulate, and calibrate dynamical systems in Python 3. Its goal is to reduce the time it takes to implement a dynamical system with $n$-dimensional states represented by coupled…
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
Multiscale modeling, which integrates material properties from ab initio calculations into continuum-scale simulations, is a promising strategy for optimizing semiconductor devices. However, a key challenge remains: while ab initio methods…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…
Jupyter Notebook is the tool of choice of many data scientists in the early stages of ML workflows. The notebook format, however, has been criticized for inducing bad programming practices; indeed, researchers have already shown that…
The yaglm package aims to make the broader ecosystem of modern generalized linear models accessible to data analysts and researchers. This ecosystem encompasses a range of loss functions (e.g. linear, logistic, quantile regression),…
Seismology has witnessed significant advancements in recent years with the application of deep learning methods to address a broad range of problems. These techniques have demonstrated their remarkable ability to effectively extract…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
We devote our studies to the subject of weakly nonintegrable dynamics of systems with a macroscopic number of degrees of freedom. Our main points of interest are the relations between the timescales of thermalization and the timescales of…
This article presents the MAGI software package for the inference of dynamic systems. The focus of MAGI is on dynamics modeled by nonlinear ordinary differential equations with unknown parameters. While such models are widely used in…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
We present a MATLAB package called the Pha-sorArray Toolbox that has been developed to make harmonic analysis and control methods both practical and user-friendly. The toolbox adopts an object-oriented architecture that enables intuitive…
Additive models offer accurate and interpretable predictions for tabular data, a critical tool for statistical modeling. Recent advances in Neural Additive Models (NAMs) allow these models to handle complex machine learning tasks, including…
Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…
This research explores the application of quadratic polynomials in Python for advanced data analysis. The study demonstrates how quadratic models can effectively capture nonlinear relationships in complex datasets by leveraging Python…