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Background: Deep learning models have shown promise in diagnosing neurodevelopmental disorders (NDD) like ASD and ADHD. However, many models either use graph neural networks (GNN) to construct single-level brain functional networks (BFNs)…

In this paper, we propose a novel Hermite weighted essentially non-oscillatory (HWENO) fast sweeping method to solve the static Hamilton-Jacobi equations efficiently. During the HWENO reconstruction procedure, the proposed method is built…

In recent years, large language models (LLMs) have made remarkable advancements, yet hallucination, where models produce inaccurate or non-factual statements, remains a significant challenge for real-world deployment. Although current…

We evaluate the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations. The methods are based on affine combinations of time-splitting integrators and…

We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high…

Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been developed to approximate their solutions. Although these…

High resolution and advanced semantic representation are both vital for dense prediction. Empirically, low-resolution feature maps often achieve stronger semantic representation, and high-resolution feature maps generally can better…

In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…

High-resolution remote sensing images (HRRSIs) contain substantial ground object information, such as texture, shape, and spatial location. Semantic segmentation, which is an important task for element extraction, has been widely used in…

High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…

In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often…

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

In this paper, we develop a physics-informed deep operator learning framework for solving multi-term time-fractional mixed diffusion-wave equations (TFMDWEs). We begin by deriving an $L_2$ approximation, which achieves first-order accuracy…

Deep Neural Network (DNN)-based image reconstruction, despite many successes, often exhibits uneven fidelity between high and low spatial frequency bands. In this paper we propose the Learning Synthesis by DNN (LS-DNN) approach where two…

In this paper, we propose a novel variable-separation (NVS) method for generic multivariate functions. The idea of NVS is extended to to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs).…

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…

High-resolution representations are essential for position-sensitive vision problems, such as human pose estimation, semantic segmentation, and object detection. Existing state-of-the-art frameworks first encode the input image as a…

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional…

We present a novel differentiable grid-based representation for efficiently solving differential equations (DEs). Widely used architectures for neural solvers, such as sinusoidal neural networks, are coordinate-based MLPs that are both…