Related papers: Learning dominant physical processes with data-dri…
Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience…
Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities observed in practice have a universal characterization…
Gaining and understanding the flow dynamics have much importance in a wide range of disciplines, e.g. astrophysics, geophysics, biology, mechanical engineering and biomedical engineering. As a reliable way in practice, especially for…
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…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…
Identifying the intrinsic coordinates or modes of the dynamical systems is essential to understand, analyze, and characterize the underlying dynamical behaviors of complex systems. For nonlinear dynamical systems, this presents a critical…
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario derived from the solution…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…
We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic…
With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…
Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural…
Recently, neural operators have emerged as powerful tools for learning mappings between function spaces, enabling data-driven simulations of complex dynamics. Despite their successes, a deeper understanding of their learning mechanisms…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
Understanding the principles of geophysical phenomena is an essential and challenging task. "Model-driven" approaches have supported the development of geophysics for a long time; however, such methods suffer from the curse of…
One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…