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Ensemble learning is a well established body of methods for machine learning to enhance predictive performance by combining multiple algorithms/models. Combinatorial Fusion Analysis (CFA) has provided method and practice for combining…
Various types of measurement techniques, such as Light Detection and Ranging (LiDAR) devices, anemometers, and wind vanes, are extensively utilized in wind energy to characterize the inflow. However, these methods typically gather data at…
A non-intrusive data assimilation methodology is developed to improve the statistical predictions of large-eddy simulations (LES). The ensemble-variational (EnVar) approach aims to minimize a cost function that is defined as the discrepancy…
Data assimilation, defined as the fusion of data with preexisting knowledge, is particularly suited to elucidating underlying phenomena from noisy/insufficient observations. Although this approach has been widely used in diverse fields,…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if we apply a…
Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides…
A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ($\simeq$15 seconds) proposed, the…
Weather forecasting is fundamentally challenged by the chaotic nature of the atmosphere, necessitating probabilistic approaches to quantify uncertainty. While traditional ensemble prediction (EPS) addresses this through computationally…
State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…
Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…
Structure-from-motion (SfM) largely relies on feature tracking. In image sequences, if disjointed tracks caused by objects moving in and out of the field of view, occasional occlusion, or image noise, are not handled well, corresponding SfM…
The ensemble Gaussian mixture filter (EnGMF) is a non-linear filter suited to data assimilation of highly non-Gaussian and non-linear models that has practical utility in the case of a small number of samples, and theoretical convergence to…
Artificial intelligence (AI)-based weather prediction research is growing rapidly and has shown to be competitive with the advanced dynamic numerical weather prediction models. However, research combining AI-based weather prediction models…
Recent advances in NeRF inpainting have leveraged pretrained diffusion models to enhance performance. However, these methods often yield suboptimal results due to their ineffective utilization of 2D diffusion priors. The limitations…
Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…
Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under…
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that…
Tsunami deposits are recordings of tsunami events that contain information about flow conditions. Deciphering quantitative information from tsunami deposits is especially important for analyzing paleo-tsunami events in which deposits…
This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…