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In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…
Anomaly detection in multivariate time series is a critical task across a wide range of real-world applications, where abnormal behaviour is rare, labels are unavailable, and the cost of a miss is high. The central challenge is learning a…
Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from…
Reliable deep learning models require not only accurate predictions but also well-calibrated confidence estimates to ensure dependable uncertainty estimation. This is crucial in safety-critical applications like autonomous driving, which…
Recently, new adaptive techniques were developed that greatly improved the efficiency of solving PDEs using spectral methods. These adaptive spectral techniques are especially suited for accurately solving problems in unbounded domains and…
Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…
When fully conservative methods are used to simulate transcritical flow, spurious pressure oscillations and numerical instability are generated. The strength and speed of propagation of shock waves cannot be represented correctly using a…
We present goal-oriented a posteriori error estimates for the automatic variationally stable finite element (AVS FE) method for scalar-valued convection-diffusion problems. The AVS-FE method is a Petrov-Galerkin method in which the test…
We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…
The application of immersed boundary methods in static analyses is often impeded by poorly cut elements (small cut elements problem), leading to ill-conditioned linear systems of equations and stability problems. While these concerns may…
The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging…
Hyperspectral data acquired through remote sensing are invaluable for environmental and resource studies. While rich in spectral information, various complexities such as environmental conditions, material properties, and sensor…
A novel method of exponentially stable adaptive control to compensate for matched parametric uncertainty under a mild condition of semi-persistent excitation (s-PE) of a regressor with piecewise-constant rank and nullspace is proposed. It…
We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized 'labeled' data, and (ii) a much larger sized 'unlabeled' data. Such data arises…
Data-driven fault diagnostics of safety-critical systems often faces the challenge of a complete lack of labeled data associated with faulty system conditions (i.e., fault types) at training time. Since an unknown number and nature of fault…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
Sparse labels have been attracting much attention in recent years. However, the performance gap between weakly supervised and fully supervised salient object detection methods is huge, and most previous weakly supervised works adopt complex…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…