相关论文: Learning Nonautonomous Systems via Dynamic Mode De…

Data-driven control methods based on subspace representations are powerful but are often limited to linear time-invariant systems where the model order is known. A key challenge is developing online data-driven control algorithms for…

Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…

Discovery of mathematical descriptors of physical phenomena from observational and simulated data, as opposed to from the first principles, is a rapidly evolving research area. Two factors, time-dependence of the inputs and hidden…

We propose a system identification method, Non-Markovian Optimization-based Modeling for Approximate Dynamics with Spatially-homogeneous memory (NOMADS), for identifying linear dynamical systems from a set of multi-dimensional time-series…

We develop a learning-based algorithm for the control of autonomous systems governed by unknown, nonlinear dynamics to satisfy user-specified spatio-temporal tasks expressed as signal temporal logic specifications. Most existing algorithms…

The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic…

Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary…

Fast and reliable surrogate models are critical for optimization, control and uncertainty analysis in geological carbon-storage projects, yet high-fidelity multiphase simulators remain too expensive. Dynamic Mode Decomposition (DMD) offers…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and…

The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…

In this paper, we propose a novel algorithm for learning the Koopman operator of a dynamical system from a \textit{small} amount of training data. In many applications of data-driven modeling, e.g. biological network modeling,…

One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…