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Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…
Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the…
We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion, subsurface flow processes, and rock physics models. For…
Estimation of near-wall turbulence in channel flow from outer observations is investigated using adjoint-variational data assimilation. We first consider fully resolved velocity data, starting at a distance from the wall. By enforcing the…
This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…
Mapping the seafloor with underwater imaging cameras is of significant importance for various applications including marine engineering, geology, geomorphology, archaeology and biology. For shallow waters, among the underwater imaging…
Variance reduction techniques are designed to decrease the sampling variance, thereby accelerating convergence rates of first-order (FO) and zeroth-order (ZO) optimization methods. However, in composite optimization problems, ZO methods…
Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…
Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates…
Time-varying parameter VARs with stochastic volatility are routinely used for structural analysis and forecasting in settings involving a few endogenous variables. Applying these models to high-dimensional datasets has proved to be…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
Seasonal weather forecasts are crucial for long-term planning in many practical situations and skillful forecasts may have substantial economic and humanitarian implications. Current seasonal forecasting models require statistical…
Adjoint-based sensitivity analysis is of interest in computational science due to its ability to compute sensitivities at a lower cost with respect to several design parameters. However, conventional sensitivity analysis methods fail in the…
Downscaling is necessary to generate high-resolution observation data to validate the climate model forecast or monitor rainfall at the micro-regional level operationally. Dynamical and statistical downscaling models are often used to get…
This paper addresses the impact of assimilating data from the Earth Networks Total Lightning Network (ENTLN) during two cases of severe weather. Data from the ENTLN serve as a substitute for those from the upcoming launch of the GOES…
Conventional SLAM systems using visual or LiDAR data often struggle in poor lighting and severe weather. Although 4D radar is suited for such environments, its sparse and noisy point clouds hinder accurate odometry estimation, while the…
In this paper, we propose a reduced order approach for 3D variational data assimilation governed by parametrized partial differential equations. In contrast to the classical 3D-VAR formulation that penalizes the measurement error directly,…
Data assimilation is the process of fusing information from imperfect computer simulations with noisy, sparse measurements of reality to obtain improved estimates of the state or parameters of a dynamical system of interest. The data…
The impact of statistical methodologies on studying groundwater has been significant in the last several decades, due to cheaper computational abilities and presence of technologies that enable us to extract and measure more and more data.…
Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…