相关论文: Data Driven Learning of Mori-Zwanzig Operators for…

Stochastic dynamics, such as molecular dynamics, are important in many scientific applications. However, summarizing and analyzing the results of such simulations is often challenging, due to the high dimension in which simulations are…

The transfer tensor method is a versatile tool for analyzing and propagating general open quantum systems. It captures in a compact manner all memory effects in a non-Markovian system through a straightforward transformation of a set of…

To investigate the impact of non-linear interactions on dynamic coarse graining, we study a simplified model system, featuring a tracer particle in a complex environment. Using a projection operator formalism and computer simulations, we…

Data-driven techniques have emerged as a promising alternative to traditional numerical methods for solving PDEs. For time-dependent PDEs, many approaches are Markovian -- the evolution of the trained system only depends on the current…

Representation learning has emerged as a crucial focus in machine and deep learning, involving the extraction of meaningful and useful features and patterns from the input data, thereby enhancing the performance of various downstream tasks…

The Fuzzy transform is ubiquitous in different research fields and applications, such as image and data compression, data mining, knowledge discovery, and the analysis of linguistic expressions. As a generalisation of the Fuzzy transform,…

We propose an Entropy-Optimal Manifold Clustering (EOMC) - and show that it mitigates the cost scaling and robustness issues of the existing dimensionality reduction and manifold learning tools in nonstationary and nonlinear situations,…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

The capabilities of recurrent neural networks and Koopman-based frameworks are assessed in the prediction of temporal dynamics of the low-order model of near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results show…

Methodologies for training machine learning potentials (MLPs) to quantum-mechanical simulation data have recently seen tremendous progress. Experimental data has a very different character than simulated data, and most MLP training…

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…

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…

We relate the memory kernel in the Nakajima-Zwanzig-Mori time-convolution approach to the reduced system propagator which is often used to obtain the kernel in the Tokuyama-Mori time-convolutionless approach. The connection provides a…

Turbulence poses challenges for numerical simulation due to its chaotic, multiscale nature and high computational cost. Traditional turbulence modeling often struggles with accuracy and long-term stability. Recent scientific machine…

The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…

Since their invention in the 1980s [1], optical tweezers have found a wide range of applications, from biophotonics and mechanobiology to microscopy and optomechanics [2, 3, 4, 5]. Simulations of the motion of microscopic particles held by…

We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…

Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design…

Turbulence modeling within the Lattice Boltzmann Method (LBM) framework has long relied on traditional algebraic sub-grid scale (SGS) models, which often suffer from over-dissipation and lack of spatial selectivity near solid boundaries. In…

Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational…