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We describe a comprehensive model for the formation and morphological development of atmospheric ice crystals growing from water vapor, also known as snow crystals. Our model derives in part from empirical measurements of the intrinsic ice…
Identifying Ordinary Differential Equations (ODEs) from measurement data requires both fitting the dynamics and assimilating, either implicitly or explicitly, the measurement data. The Sparse Identification of Nonlinear Dynamics (SINDy)…
The problem of testing hypothesis that a density function has no more than $\mu$ derivatives versus it has more than $\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal…
In many fields of application, dynamic processes that evolve through time are well described by systems of ordinary differential equations (ODEs). The analytical solution of the ODEs is often not available and different methods have been…
In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has…
While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…
Weather forecasting centers currently rely on statistical postprocessing methods to minimize forecast error. This improves skill but can lead to predictions that violate physical principles or disregard dependencies between variables, which…
Understanding the dynamic behavior of polar fluids is essential for modeling complex systems such as electrolytes and biological media. In this work, we develop and apply a Stochastic Density Functional Theory (SDFT) framework to describe…
The functional linear model is a popular tool to investigate the relationship between a scalar/functional response variable and a scalar/functional covariate. We generalize this model to a functional linear mixed-effects model when repeated…
We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a…
To fully exploit the benefits of the fog environment, efficient management of data locality is crucial. Blind or reactive data replication falls short in harnessing the potential of fog computing, necessitating more advanced techniques for…
Smoothing is widely used approach for measurement noise reduction in spectral analysis. However, it suffers from signal distortion caused by peak suppression. A locally self-adjustive smoothing method is developed that retains sharp peaks…
Snow depth plays a central role in seasonal snowpack characterization and the terrestrial water cycle, yet remains challenging to estimate at high spatial resolution. Recent studies have shown that repeat-pass interferometric synthetic…
Current system thermal-hydraulic codes have limited credibility in simulating real plant conditions, especially when the geometry and boundary conditions are extrapolated beyond the range of test facilities. This paper proposes a…
Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over…
To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…
In engineering applications snow often undergoes large and fast deformations. During these deformations the snow transforms from a sintered porous material into a granular material. In order to capture the fundamental mechanical behavior of…
Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
Score matching is a popular method for estimating unnormalized statistical models. However, it has been so far limited to simple, shallow models or low-dimensional data, due to the difficulty of computing the Hessian of log-density…