相关论文: Learning the Dynamics of Physical Systems from Spa…

We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing data, sparse observations, or adaptive computational…

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…

Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown…

Physical dynamical systems can be viewed as natural information processors: their systems preserve, transform, and disperse input information. This perspective motivates learning not only from data generated by such systems, but also how to…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a…

Leveraging physical knowledge described by partial differential equations (PDEs) is an appealing way to improve unsupervised video prediction methods. Since physics is too restrictive for describing the full visual content of generic…

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…

Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…

Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…

Structural failures are often caused by catastrophic events such as earthquakes and winds. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real time. Currently available high-fidelity…

We investigate methods for learning partial differential equation (PDE) models from spatiotemporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select…