Related papers: Data-driven transient growth analysis
Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
Non-modal transient growth of disturbances in a viscous mixing layer flow is studied for the Reynolds numbers varying from 100 up to 5000 at different streamwise and spanwise wavenumbers. By comparing results of several mathematical…
This paper presents data-driven implementations of balanced truncation and several of its generalizations that rely exclusively on transfer function samples on the imaginary axis. Rather than implicitly approximating the Gramians via…
We develop the framework for a non-intrusive, quadrature-based method for approximate balanced truncation (QuadBT) of linear systems with quadratic outputs, thus extending the applicability of QuadBT, which was originally designed for…
In this paper, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
Avoiding aliasing in time-resolved flow data obtained through high fidelity simulations while keeping the computational and storage costs at acceptable levels is often a challenge. Well-established solutions such as increasing the sampling…
This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved…
The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
The contributions of this technical note are twofold. Firstly, we formulate an optimization problem to obtain a linear representation of a nonlinear vector field based on a system's trajectory. We also prove that its cost function is…
Certain neural network architectures, in the infinite-layer limit, lead to systems of nonlinear differential equations. Motivated by this idea, we develop a framework for analyzing time signals based on non-autonomous dynamical equations.…
Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized…
Deep learning is widely applied in computer-aided pathological diagnosis, which alleviates the pathologist workload and provide timely clinical analysis. However, most models generally require large-scale annotated data for training, which…
We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to…
In this paper, we investigate a continuous-time linear quadratic control problem for systems with unknown matrices, where only input-output data are available. We propose an output-feedback learning framework based on a canonical nonminimal…
The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. This is entirely a data-driven approach that extracts all necessary information from data snapshots which are commonly supposed to be sampled…