Related papers: Physics-informed Autoencoders for Lyapunov-stable …

Well-calibrated traffic flow models are fundamental to understanding traffic phenomena and designing control strategies. Traditional calibration has been developed base on optimization methods. In this paper, we propose a novel…

In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…

The use of deep learning methods for modeling fluid flow has drawn a lot of attention in the past few years. In situations where conventional numerical approaches can be computationally expensive, these techniques have shown promise in…

We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Invariance and stability are essential notions in dynamical systems study, and thus it is of great interest to learn a dynamics model with a stable invariant set. However, existing methods can only handle the stability of an equilibrium. In…

Computational fluid dynamics (CFD) drives progress in numerous scientific and engineering fields, yet high-fidelity simulations remain computationally prohibitive. While machine learning approaches offer computing acceleration, they…

This work introduces a new neural model which follows the transport equation by design. A physical problem, the Taylor-Green vortex, defined on a bi-periodic domain, is used as a benchmark to evaluate the performance of both the standard…

Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this letter, we introduce a modular physics guided…

Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion…

Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…

The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…

Control Lyapunov function is a central tool in stabilization. It generalizes an abstract energy function -- a Lyapunov function -- to the case of controlled systems. It is a known fact that most control Lyapunov functions are non-smooth --…

While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity…

Stability certificates play a critical role in ensuring the safety and reliability of robotic systems. However, deriving these certificates for complex, unknown systems has traditionally required explicit knowledge of system dynamics, often…

Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state.…

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…

System identification in control theory aims to approximate dynamical systems from trajectory data. While neural networks have demonstrated strong predictive accuracy, they often fail to preserve critical physical properties such as…

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…