Related papers: Hybrid Iterative Neural Low-Regularity Integrator …

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…

Model-based deep learning methods such as loop unrolling (LU) and deep equilibrium model}(DEQ) extensions offer outstanding performance in solving inverse problems (IP). These methods unroll the optimization iterations into a sequence of…

Edge intelligence is constrained by the energy and latency costs of shuttling data through electronic memory hierarchies. Optical systems offer a fundamentally different computational regime: once an input wavefront is launched into a…

Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We…

Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in the input is the Lipschitz constant of the input-output map…

Hyperspectral image (HSI) restoration aims at recovering clean images from degraded observations and plays a vital role in downstream tasks. Existing model-based methods have limitations in accurately modeling the complex image…

High-fidelity binaural audio synthesis is crucial for immersive listening, but existing methods require extensive computational resources, limiting their edge-device application. To address this, we propose the Lightweight Implicit Neural…

The probabilistic diffusion model (DM), generating content by inferencing through a recursive chain structure, has emerged as a powerful framework for visual generation. After pre-training on enormous data, the model needs to be properly…

We consider the problem of linear classification under general loss functions in the limited-data setting. Overfitting is a common problem here. The standard approaches to prevent overfitting are dimensionality reduction and regularization.…

We present an $\ell^2_2+\ell_1$-regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Hybrid systems have steadily grown in popularity over the last few decades because they ease the task of modeling complicated nonlinear systems. Legged locomotion, robotic manipulation, and additive manufacturing are representative examples…

Neural networks suffer from spectral bias having difficulty in representing the high frequency components of a function while relaxation methods can resolve high frequencies efficiently but stall at moderate to low frequencies. We exploit…

We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity, parabolic, hyperbolic and Stokes equations; and a PDE…

Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule…

Heterogeneous Information Network (HIN) embedding refers to the low-dimensional projections of the HIN nodes that preserve the HIN structure and semantics. HIN embedding has emerged as a promising research field for network analysis as it…

We present the hidden-layer concatenated physics informed neural network (HLConcPINN) method, which combines hidden-layer concatenated feed-forward neural networks, a modified block time marching strategy, and a physics informed approach…

A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…