Related papers: Finding nonlinear system equations and complex net…

Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…

Dynamic community detection concerns inferring how community memberships evolve over time, including the emergence, persistence, merging, and dissolution of groups in temporal networks. We propose a Bayesian nonparametric model for…

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…

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…

Accurate and concise governing equations are crucial for understanding system dynamics. Recently, data-driven methods such as sparse regression have been employed to automatically uncover governing equations from data, representing a…

In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the…

Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…

We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…

The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points…

Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…