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Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce…

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other nonsmooth. The key highlight is a natural property of the resulting problem's structure that yields a…

We provide some basic and sensible definitions of different types of digital twins and recommendations on when and how to use them. Following up on our recent publication of the Learning Causal Digital Twin, this article reports on a…

This paper introduces two new algorithms to accurately estimate the process noise covariance of a discrete-time Kalman filter online for robust orbit determination in the presence of dynamics model uncertainties. Common orbit determination…

In this paper, we use the optimization formulation of nonlinear Kalman filtering and smoothing problems to develop second-order variants of iterated Kalman smoother (IKS) methods. We show that Newton's method corresponds to a recursion over…

For recursive circular filtering based on circular statistics, we introduce a general framework for estimation of a circular state based on different circular distributions, specifically the wrapped normal distribution and the von Mises…

Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained…

Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…

Two-time-scale Stochastic Approximation (SA) is an iterative algorithm with applications in reinforcement learning and optimization. Prior finite time analysis of such algorithms has focused on fixed point iterations with mappings…

Symbolic regression (SR) has emerged as a pivotal technique for uncovering the intrinsic information within data and enhancing the interpretability of AI models. However, current state-of-the-art (sota) SR methods struggle to perform…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

The Kalman filter (KF) provides optimal recursive state estimates for linear-Gaussian systems and underpins applications in control, signal processing, and others. However, it is vulnerable to outliers in the measurements and process noise.…

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…

In this paper, a two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel is proposed to reduce the computation time and improve the accuracy of the scheme…

We present a machine learning-based mesh refinement technique for steady and unsteady flows. The clustering technique proposed by Otmani et al. arXiv:2207.02929 [physics.flu-dyn] is used to mark the viscous and turbulent regions for the…

This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…