Related papers: The Adaptive Solution of High-Frequency Helmholtz …

Increasing attention is being paid to millimeter-wave (mmWave), 30 GHz to 300 GHz, and terahertz (THz), 300 GHz to 10 THz, sensing applications including security sensing, industrial packaging, medical imaging, and non-destructive testing.…

In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs),…

This paper aims to address a common challenge in deep learning-based image transformation methods, such as image enhancement and super-resolution, which heavily rely on precisely aligned paired datasets with pixel-level alignments. However,…

In this paper we propose a discontinuous Galerkin plane wave neural network (DGPWNN) method for approximately solving Helmholtz equation and Maxwell's equations. In this method, we define an elliptic-type variational problem as in the plane…

Non-determinism and non-reproducibility present significant challenges in deep learning, leading to inconsistent results across runs and platforms. These issues stem from two origins: random number generation and floating-point computation.…

This work presents, to the best of the authors' knowledge, the first generalizable and fully data-driven adaptive framework designed to stabilize deep learning (DL) autoregressive forecasting models over long time horizons, with the goal of…

Graph deep learning (GDL) has demonstrated impressive performance in predicting population-based brain disorders (BDs) through the integration of both imaging and non-imaging data. However, the effectiveness of GDL based methods heavily…

Resonance is instrumental in modern optics and photonics for novel phenomena such as cavity quantum electrodynamics and electric-field-induced transparency. While one can use numerical simulations to sweep geometric and material parameters…

In modern biomedical and econometric studies, longitudinal processes are often characterized by complex time-varying associations and abrupt regime shifts that are shared across correlated outcomes. Standard functional data analysis (FDA)…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…

Terahertz ultra-massive MIMO (THz UM-MIMO) is envisioned as one of the key enablers of 6G wireless networks, for which channel estimation is highly challenging. Traditional analytical estimation methods are no longer effective, as the…

Solving high-dimensional Fokker-Planck (FP) equations is a challenge in computational physics and stochastic dynamics, due to the curse of dimensionality (CoD) and unbounded domains. Existing deep learning approaches, such as…

The Helmholtz scattering problem with high wave number is truncated by the perfectly matched layer (PML) technique and then discretized by the linear continuous interior penalty finite element method (CIP-FEM). It is proved that the…

A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…

Deep learning has revolutionized biomedical research by providing sophisticated methods to handle complex, high-dimensional data. Multimodal deep learning (MDL) further enhances this capability by integrating diverse data types such as…

For millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, hybrid processing architecture is essential to significantly reduce the complexity and cost but is quite challenging to be jointly optimized over the…

Chebyshev pseudospectral (PS) methods are reported to provide highly accurate solution using polynomial approximation. Use of polynomial basis functions in PS algorithms limits the formulation to univariate systems constraining it to tensor…

We present a ray-based finite element method (ray-FEM) by learning basis adaptive to the underlying high-frequency Helmholtz equation in smooth media. Based on the geometric optics ansatz of the wave field, we learn local dominant ray…