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A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential…
Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate.…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…
Automatic medical image segmentation is a fundamental step in computer-aided diagnosis, yet fully supervised approaches demand extensive pixel-level annotations that are costly and time-consuming. To alleviate this burden, we propose a…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
Weakly supervised semantic segmentation (WSSS) aims to produce pixel-wise class predictions with only image-level labels for training. To this end, previous methods adopt the common pipeline: they generate pseudo masks from class activation…
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed…
The adaptive coherence estimator (ACE) estimates the squared cosine of the angle between a known target vector and a sample vector in a whitened coordinate space. The space is whitened according to an estimation of the background…
Continuous-time approximation of Stochastic Gradient Descent (SGD) is a crucial tool to study its escaping behaviors from stationary points. However, existing stochastic differential equation (SDE) models fail to fully capture these…
Accurate measurement of light wavelength is critical for applications in spectroscopy, optical communication, and semiconductor manufacturing, ensuring precision and consistency of sensing, high-speed data transmission and device…
In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods…
Photonic systems with exceptional points, where eigenvalues and corresponding eigenstates coalesce, have attracted interest due to their topological features and enhanced sensitivity to external perturbations. Non-Hermitian mode-coupling…
Diffusion models have emerged as powerful learned priors for solving inverse problems. However, current iterative solving approaches which alternate between diffusion sampling and data consistency steps typically require hundreds or…
Optimizing multimodal waveguide performance depends on modal analysis; however, existing methods focus predominantly on modal power distribution (MPD) and, limited by experimental hardware and conditions, exhibit low accuracy, poor…
Maximizing the user-item engagement based on vectorized embeddings is a standard procedure of recent recommender models. Despite the superior performance for item recommendations, these methods however implicitly deprioritize the modeling…
To achieve reliable mining results for massive vessel trajectories, one of the most important challenges is how to efficiently compute the similarities between different vessel trajectories. The computation of vessel trajectory similarity…
The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…
The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…
Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and…