Related papers: Determining Modes, State Reconstruction, and Inter…

We study the local controllability properties of 2D and 3D bio-mimetic swimmers employing the change of their geometric shape to propel themselves in an incompressible fluid described by Navier-Stokes equations. It is assumed that swimmers'…

We study the problem of identifying the parameters of a linear system from its response to multiple unknown waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the…

Deep learning Networks play a crucial role in the evolution of a vast number of current machine learning models for solving a variety of real world non-trivial tasks. Such networks use big data which is generally unlabeled unsupervised and…

We study a nonlinear-nudging modification of the Azouani-Olson-Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier-Stokes equations. We give a rigorous proof that the nonlinear-nudging system is…

This paper introduces a deep learning-based super-resolution (SR) framework specifically developed for accurately reconstructing high-resolution velocity fields in two-way coupled particle-laden turbulent flows. Leveraging conditional…

In this work the issue of whether key energetic properties (nonlinear, exponential-type dissipation in the abscence of forcing and long-term stability under conditions of time dependent loading) are automatically inherited by deforming…

We present an adaptive algorithm that guarantees synchronization in diffusively coupled systems. We first consider compartmental systems of ODEs, where each compartment represents a spatial domain of components interconnected through…

We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of…

The question of how and why the phenomenon of mode connectivity occurs in training deep neural networks has gained remarkable attention in the research community. From a theoretical perspective, two possible explanations have been proposed:…

Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it…

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…

Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in…

We describe a spectrally-filtered discrete-in-time downscaling data assimilation algorithm and prove, in the context of the two-dimensional Navier--Stokes equations, that this algorithm works for a general class of interpolants, such as…

We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method…

This paper presents tailor-made neural model structures and two custom fitting criteria for learning dynamical systems. The proposed framework is based on a representation of the system behavior in terms of continuous-time state-space…

For the two-phase incompressible Navier--Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify…

We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of…

Symmetrization of topologically ordered wavefunctions is a powerful method for constructing new topological models. Here, we study wavefunctions obtained by symmetrizing quantum double models of a group $G$ in the Projected Entangled Pair…

Using diffusion Monte Carlo (DMC) and density functional theory (DFT) calculations, we examined the structural stability and interlayer binding properties of PtSe$_2$, a representative transition metal dichalcogenide (TMD) with strong…

Recent theoretical models of diffusion processes, conceptualized as coupled Ornstein-Uhlenbeck systems, predict a hierarchy of interaction timescales, and consequently, the existence of a synchronization gap between modes that commit at…