Related papers: A Neural Operator based on Dynamic Mode Decomposit…
Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…
We utilize machine learning models which are based on recurrent neural networks to optimize dynamical decoupling (DD) sequences. DD is a relatively simple technique for suppressing the errors in quantum memory for certain noise models. In…
A data-driven and equation-free approach is proposed and discussed to model ships maneuvers in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear…
Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerged as a powerful tool for solving PDEs, leveraging their…
The Dynamic Mode Decomposition (DMD) and the more general Extended DMD (EDMD) are powerful tools for computational analysis of dynamical systems in data-driven scenarios. They are built on the theoretical foundation of the Koopman…
Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit timeseries data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coherent modes that evolve in time according to exponential…
Dynamic Mode Decomposition (DMD) is a data-driven method related to Koopman operator theory that extracts information about dominant dynamics from data snapshots. In this paper we examine techniques to accelerate the application of DMD to…
Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time diagonal of such a…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…
This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability…
This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…
Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…
A dynamic mode decomposition (DMD) based reduced-order model (ROM) is developed for tracking, detection, and prediction of kinetic plasma behavior. DMD is applied to the high-fidelity kinetic plasma model based on the electromagnetic…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
Irrespective of the fact that Machine learning has produced groundbreaking results, it demands an enormous amount of data in order to perform so. Even though data production has been in its all-time high, almost all the data is unlabelled,…
Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…
Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…
Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…
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…
The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…