相关论文: Gaussian process regression and conditional Karhun…

A discrete-time conditional Gaussian Koopman network (CGKN) is developed in this work to learn surrogate models that can perform efficient state forecast and data assimilation (DA) for high-dimensional complex dynamical systems, e.g.,…

We propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems as a function of the systems' spatially heterogeneous parameter fields with applications to uncertainty quantification…

In this work we are interested in the (ill-posed) inverse problem for absolute permeability characterization that arises in predictive modeling of porous media flows. We consider a Bayesian statistical framework with a preconditioned Markov…

Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…

We present a sequential data assimilation algorithm based on the ensemble Kalman inversion to estimate the near-surface shear wave velocity profile and damping when heterogeneous data and a priori information that can be represented in…

Gaussian random field is a ubiquitous model for spatial phenomena in diverse scientific disciplines. Its approximation is often crucial for computational feasibility in simulation, inference, and uncertainty quantification. The…

This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to…

We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space…

We propose a physics-informed machine learning method for uncertainty quantification in high-dimensional inverse problems. In this method, the states and parameters of partial differential equations (PDEs) are approximated with truncated…

Deep learning is widely used to predict complex dynamical systems in many scientific and engineering areas. However, the black-box nature of these deep learning models presents significant challenges for carrying out simultaneous data…

We apply the Karhunen-Lo\'eve methods to cosmic microwave background (CMB) data sets, and show that we can recover the input cosmology and obtain the marginalized likelihoods in $\Lambda$ cold dark matter cosmologies in under a minute, much…

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…

This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samples to get a…

The Ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 [10] as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application…

Data assimilation methods aim at estimating the state of a system by combining observations with a physical model. When sequential data assimilation is considered, the joint distribution of the latent state and the observations is described…

Practical data assimilation algorithms often contain hyper-parameters, which may arise due to, for instance, the use of certain auxiliary techniques like covariance inflation and localization in an ensemble Kalman filter, the…

A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…

Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…

In this paper we use Gaussian processes (kernel methods) to learn mappings between trajectories of distinct differential equations. Our goal is to simplify both the representation and the solution of these equations. We begin by examining…