Related papers: Can Machine Learning Identify Governing Laws For D…

High-fidelity quantum dynamics emulators can be used to predict the time evolution of complex physical systems. Here, we introduce an efficient training framework for constructing machine learning-based emulators. Our approach is based on…

Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…

The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable the…

First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured…

In chemical engineering, process data are expensive to acquire, and complex phenomena are difficult to fully model. We explore the use of physics-informed neural networks (PINNs) for modeling dynamic processes with incomplete mechanistic…

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…

Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…

The discovery of dynamical models from data represents a crucial step in advancing our understanding of physical systems. Library-based sparse regression has emerged as a powerful method for inferring governing equations directly from…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. In this paper, we…

Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recently…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. In this paper, we argue that this makes SINDy a potentially useful tool for causal discovery and that existing…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Atmospheric modeling has recently experienced a surge with the advent of deep learning. Most of these models, however, predict concentrations of pollutants following a data-driven approach in which the physical laws that govern their…

Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related…