Related papers: PCG-Informed Neural Solvers for High-Resolution Ho…

The widely-adopted practice is to train deep learning models with specialized hardware accelerators, e.g., GPUs or TPUs, due to their superior performance on linear algebra operations. However, this strategy does not employ effectively the…

Graph Convolutional Neural Network (GCNN) is a popular class of deep learning (DL) models in material science to predict material properties from the graph representation of molecular structures. Training an accurate and comprehensive GCNN…

We propose Gradient Informed Neural Networks (GradINNs), a methodology inspired by Physics Informed Neural Networks (PINNs) that can be used to efficiently approximate a wide range of physical systems for which the underlying governing…

Composed Image Retrieval (CIR) enables image search by combining a reference image with modification text. Intrinsic noise in CIR triplets incurs intrinsic uncertainty and threatens the model's robustness. Probabilistic learning approaches…

Heterogeneous graph neural network has unleashed great potential on graph representation learning and shown superior performance on downstream tasks such as node classification and clustering. Existing heterogeneous graph learning networks…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…

Determining effective elastic properties of rocks from their pore-scale digital images is a key goal of digital rock physics (DRP). Direct numerical simulation (DNS) of elastic behavior, however, incurs high computational cost; and…

In multi-task learning (MTL), gradient conflict poses a significant challenge. Effective methods for addressing this problem, including PCGrad, CAGrad, and GradNorm, in their original implementations are computationally demanding, which…

The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…

Graph convolution networks (GCNs) are extensively utilized in various graph tasks to mine knowledge from spatial data. Our study marks the pioneering attempt to quantitatively investigate the GCN robustness over omnipresent heterophilic…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…

Predicting the dynamic behaviors of particles in suspension subject to hydrodynamic interaction (HI) and external drive can be critical for many applications. By harvesting advanced deep learning techniques, the present work introduces a…

Eigenvalue problems have a distinctive forward-inverse structure and are fundamental to characterizing a system's thermal response, stability, and natural modes. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative for…

Despite the success of Heterogeneous Graph Neural Networks (HGNNs) in modeling real-world Heterogeneous Information Networks (HINs), challenges such as expressiveness limitations and over-smoothing have prompted researchers to explore Graph…

We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through…

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized…

This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…