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In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method…
Understanding the sources that contribute to fine particulate matter (PM$_{2.5}$) is of crucial importance for designing and implementing targeted air pollution mitigation strategies. Determining what factors contribute to a pollutant's…
Shale gas plays an important role in reducing pollution and adjusting the structure of world energy. Gas content estimation is particularly significant in shale gas resource evaluation. There exist various estimation methods, such as first…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of…
Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution…
Scene graph generation aims to capture detailed spatial and semantic relationships between objects in an image, which is challenging due to incomplete labelling, long-tailed relationship categories, and relational semantic overlap. Existing…
Lagrangian-based methods are classical methods for solving convex optimization problems with equality constraints. We present novel prediction-correction frameworks for such methods and their variants, which can achieve $O(1/k)$ non-ergodic…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
In practice, environments constantly change over time and space, posing significant challenges for object detectors trained based on a closed-set assumption, i.e., training and test data share the same distribution. To this end, continual…
Mass determinations from gravitational lensing shear and the higher order estimator flexion are both subject to the mass sheet degeneracy. Mass sheet degeneracy refers to a transformation that leaves the reduced shear and flexion invariant.…
Stochastic generators are useful for estimating climate impacts on various sectors. Projecting climate risk in various sectors, e.g. energy systems, requires generators that are accurate (statistical resemblance to ground-truth), reliable…
We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant).…
An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…
Atmosphere light value is a highly critical parameter in defogging algorithms that are based on an atmosphere scattering model. Any error in atmosphere light value will produce a direct impact on the accuracy of scattering computation and…
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…