Related papers: Building symmetries into data-driven manifold dyna…

High-fidelity modeling of blood flow is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from…

The potential for data-driven applications to scale-resolving simulations of turbulent flows is assessed herein. Multigrid sequential data assimilation algorithms have been used to calibrate solvers for Large Eddy Simulation for the…

The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…

Flow-based models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data space that they natively reside in, rather inhabiting a…

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models…

The basic system of differential equations for a multiphase flow with the introduction of the probability of each phase in the flow is considered. The main analysis is focused on the case of a heterogeneous two-phase flow. The conservation…

More often than not, there is a need to understand the structure of complex computer code: what functions and in what order they are called, how information travels around static, input, and output variables, what depends on what. As a…

In the era of big data, managing dynamic data flows efficiently is crucial as traditional storage models struggle with real-time regulation and risk overflow. This paper introduces Data Dams, a novel framework designed to optimize data…

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…

The detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems.…

Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…

A new approach called Flow Curvature Method has been recently developed in a book entitled Differential Geometry Applied to Dynamical Systems. It consists in considering the trajectory curve, integral of any n-dimensional dynamical system…

Accurate and efficient fluid flow models are essential for applications relating to many physical phenomena including geophysical, aerodynamic, and biological systems. While these flows may exhibit rich and multiscale dynamics, in many…

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

We propose a framework for a global description of the dynamics of complex flows via clusterized spatial representations of the flow, isolating and identifying local dynamics, retrieving different Space-Time Cluster-Based Network Models…

We introduce a data-driven dynamic factor framework for modeling the joint evolution of high-dimensional covariates and responses without parametric assumptions. Standard factor models applied to covariates alone often lose explanatory…

The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these…