Related papers: Bayesian autoencoders for data-driven discovery of…
Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…
The stability and control of Unmanned Aerial Vehicles (UAVs) in a turbulent environment is a matter of great concern. Devising a robust control algorithm to reject disturbances is challenging due to the highly nonlinear nature of wind…
The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited great success to learn and predict dynamical systems from…
In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of a minimum…
This paper deals with the error processing problem of sparse identification of nonlinear dynamical systems(SINDy) through introducing the $L_\infty$ approximation to take place of the former $L_2$ approximation. The motivation is that the…
Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential…
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…
We present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the…
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…
Is there really much more to say about sparse autoencoders (SAEs)? Autoencoders in general, and SAEs in particular, represent deep architectures that are capable of modeling low-dimensional latent structure in data. Such structure could…
The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered a new wave of developments in the related…
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.…
Autoencoders receive latent models of input data. It was shown in recent works that they also estimate probability density functions of the input. This fact makes using the Bayesian decision theory possible. If we obtain latent models of…
Scientific datasets present unique challenges for machine learning-driven compression methods, including more stringent requirements on accuracy and mitigation of potential invalidating artifacts. Drawing on results from compressed sensing…
Autoencoders are neural network formulations where the input and output of the network are identical and the goal is to identify the hidden representation in the provided datasets. Generally, autoencoders project the data nonlinearly onto a…
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on…
Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…
Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem…
Rheology plays a pivotal role in understanding the flow behavior of fluids by discovering governing equations that relate deformation and stress, known as constitutive equations. Despite the importance of these equations, current methods…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…