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We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two…

Mechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness and changes to external forcing.…

With the growing number of wind farms over the last decades and the availability of large datasets, research in wind-farm flow modeling - one of the key components in optimizing the design and operation of wind farms - is shifting towards…

Many recent machine learning models rely on fine-grained dynamic control flow for training and inference. In particular, models based on recurrent neural networks and on reinforcement learning depend on recurrence relations, data-dependent…

Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscillation timing and entrainment are of interest.…

Data-driven spatial filtering algorithms optimize scores such as the contrast between two conditions to extract oscillatory brain signal components. Most machine learning approaches for filter estimation, however, disregard within-trial…

Deformable microchannels emulate a key characteristic of soft biological systems and flexible engineering devices: the flow-induced deformation of the conduit due to slow viscous flow within. Elucidating the two-way coupling between…

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…

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…

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…

Turbulence remains one of the last unresolved problems of classical physics and a major bottleneck to accurate flow prediction in climate, aerospace, and energy systems. Industrial simulations therefore rely on averaged representations of…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

High-fidelity modeling of turbulent flows is one of the major challenges in computational physics, with diverse applications in engineering, earth sciences and astrophysics, among many others. The rising popularity of high-fidelity…

Cyclic motions in vertebrates, including heart beating, breathing and walking, are derived by a network of biological oscillators having fascinating features such as entrainment, environment adaptation, and robustness. These features…

We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For…

There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…

The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states, which are visited subsequently by the system in a Markov-type hopping process. In the present work, we analyze the…

Advanced nuclear reactors often exhibit complex thermal-fluid phenomena during transients. To accurately capture such phenomena, a coarse-mesh three-dimensional (3-D) modeling capability is desired for modern nuclear-system code. In the…

Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales.…

Systematic discovery of reduced-order closure models for multi-scale processes remains an important open problem in complex dynamical systems. Even when an effective lower-dimensional representation exists, reduced models are difficult to…