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We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties…

We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

Estimating the location of N coordinates in a P dimensional Euclidean space from pairwise distances (or proximity measurements), is a principal challenge in a wide variety of fields. Conventionally, when localizing a static network of…

Recent years have seen a surge of interest in the algorithmic estimation of stochastic entropy production (EP) from trajectory data via machine learning. A crucial element of such algorithms is the identification of a loss function whose…

In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…

In this paper we consider trajectory tracking problem for robotic systems affected by unknown external perturbations. Considering possible solutions, we restrict our attention to composite adaptation, which, particularly, ensures parametric…

Nuclear liquid drop model is revisited and an explicit introduction of the surface-curvature terms is presented. The corresponding parameters of the extended classical energy formula are adjusted to the contemporarily known nuclear binding…

We consider a Johnson-N\'ed\'elec FEM-BEM coupling, which is a direct and non-symmetric coupling of finite and boundary element methods, in order to solve interface problems for the magnetostatic Maxwell's equations with the magnetic vector…

There are many application papers that solve elliptic boundary value problems by meshless methods, and they use various forms of generalized stiffness matrices that approximate derivatives of functions from values at scattered nodes…

Understanding the long-term transport of hydrogen isotopes in plasma-facing materials, such as tungsten, is critical for the steady-state operation of magnetic confinement fusion reactors. However, dynamically updating the transition…

Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric…

We develop a new, efficient, and accurate method to simulate frequency-domain borehole electromagnetic (EM) measurements acquired in the presence of three-dimensional (3D) variations of the anisotropic subsurface conductivity. The method is…

We present a numerical stability analysis of the immersed boundary(IB) method for a special case which is constructed so that Fourier analysis is applicable. We examine the stability of the immersed boundary method with the discrete Fourier…

Machine-learned coarse-grained (CG) models often suffer from noisy training data, limiting their accuracy and transferability. We propose a method to generate low-noise training data based on the potential of mean force by constraining CG…

Anomaly detection tools and methods present a key capability in modern cyberphysical and failure prediction systems. Despite the fast-paced development in deep learning architectures for anomaly detection, model optimization for a given…

While deep neural networks provide good performance for a range of challenging tasks, calibration and uncertainty estimation remain major challenges, especially under distribution shift. In this paper, we propose the amortized conditional…

This paper proposes a new nonlinear stability analysis for the acceleration-based robust position control of robot manipulators by using Disturbance Observer (DOb). It is shown that if the nominal inertia matrix is properly tuned in the…

Minimum energy path (MEP) search is a vital but often very time-consuming method to predict the transition states of versatile dynamic processes in chemistry, physics, and materials science. In this study, we reveal that the chemical bond…

We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…