Related papers: Spectral Properties of Effective Dynamics from Con…
In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation,…
This paper presents transient numerical simulations of hydraulic systems in engineering applications using the spectral element method (SEM). Along with a detailed description of the underlying numerical method, it is shown that the SEM…
Optical micro-manipulation techniques has evolved into powerful tools to efficiently steer the motion of microscopical particles on periodic and quasi-periodic potentials, driven by the external electromagnetic field. Here, the dynamics of…
For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams and evaluation rules from effective transition operators that give exact transition…
The paper develops the Loewner approach for data-based modeling of a linear distributed-parameter system. This approach is applied to a controlled flexible beam model coupled with a spring-mass system. The original dynamical system is…
An improved method for driving a system into a desired distribution, for example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an artificial relaxation process. The standard techniques for achieving the Gibbs-Boltzmann…
We introduce a novel framework to approximate the aggregate frequency dynamics of coherent generators. By leveraging recent results on dynamics concentration of tightly connected networks, and frequency weighted balanced truncation, a…
The goal of this work is to analyze the long-term behavior of reaction-diffusion systems arising in two-species chemical models and to identify the minimal set of modes that determine their dynamics. The models considered include, as…
The time-convolutionless master equation provides a general framework to model non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative…
Sampling the phase space of molecular systems -- and, more generally, of complex systems effectively modeled by stochastic differential equations -- is a crucial modeling step in many fields, from protein folding to materials discovery.…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…
We introduce a novel approach for decomposing and learning every scale of a given multiscale objective function in $\mathbb{R}^d$, where $d\ge 1$. This approach leverages a recently demonstrated implicit bias of the optimization method of…
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…
Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly…
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…
We investigate some structural properties of an efficient feedback law that stabilize linear time-reversible systems with an arbitrarily large decay rate. After giving a short proof of the generation of a group by the closed-loop operator,…
Diffusion models have emerged as powerful tools for high-quality image generation and editing, but guiding these models to produce specific outputs remains a challenge. Conventional approaches rely on conditioning mechanisms, such as text…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid.…
We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows…