Related papers: The finite expression method for turbulent dynamic…
Turbulence is characterised by chaotic dynamics and a high-dimensional state space, which make this phenomenon challenging to predict. However, turbulent flows are often characterised by coherent spatiotemporal structures, such as vortices…
The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, in its simplest form, to the Maximum…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
An understanding of the hydrodynamics of multiphase processes is essential for their design and operation. Multiphase computational fluid dynamics (CFD) simulations enable researchers to gain insight which is inaccessible experimentally.…
Models (i.e., governing equations) are fundamental to science and engineering. Advances in data acquisition now make it possible to extract interpretable, low dimensional descriptions from high dimensional observations. However, existing…
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…
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…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps. The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are…
We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…
Video-based automatic depression analysis provides a fast, objective and repeatable self-assessment solution, which has been widely developed in recent years. While depression clues may be reflected by human facial behaviours of various…
We show that extremal dynamics is very well modelled by the "Linear Fractional Stable Motion" (LFSM), a stochastic process entirely defined by two exponents that take into account spatio-temporal correlations in the distribution of active…
Low-fidelity analytical models of turbine wakes have traditionally been used for wind farm planning, performance evaluation, and demonstrating the utility of advanced control algorithms in increasing the annual energy production. In…
In turbulent flows, energy production is associated with highly organized structures, known as coherent structures. Since these structures are three-dimensional, their detection remains challenging in the most common situation, when…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…