Related papers: Multiscale DeepONet for Nonlinear Operators in Osc…
We introduce a deep neural network (DNN) framework called the \textbf{r}eal-space \textbf{a}tomic \textbf{d}ecomposition \textbf{net}work (\textsc{radnet}), which is capable of making accurate polarization and static dielectric function…
Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…
DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite dimensional Banach spaces. We analyze DeepONets and prove estimates on the resulting approximation and generalization errors. In…
Burn injuries present a significant global health challenge. Among the most severe long-term consequences are contractures, which can lead to functional impairments and disfigurement. Understanding and predicting the evolution of post-burn…
Despite the remarkable capabilities of deep neural networks in image recognition, the dependence on activation functions remains a largely unexplored area and has yet to be eliminated. On the other hand, Polynomial Networks is a class of…
Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of…
Regression with non-Euclidean responses -- e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions -- has become increasingly important in modern applications. In this paper, we propose deep…
Convolutional neural networks (CNNs) are deep learning frameworks which are well-known for their notable performance in classification tasks. Hence, many skeleton-based action recognition and segmentation (SBARS) algorithms benefit from…
Diffractive neural network (DNN), which can perform machine learning tasks based on the light propagation and diffraction, has recently emerged as a promising optical computing paradigm due to its high parallel processing speed and low…
Deep Operator Networks (DeepONets) provide a branch-trunk neural architecture for approximating nonlinear operators acting between function spaces. In the classical operator approximation framework, the input is a function $u\in C(K_1)$…
We introduce \emph{Dynamical Physics-Modeled Neural Networks} (DynPMNNs), a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation. Unlike classical feed-forward…
Dendrites are crucial structures for computation of an individual neuron. It has been shown that the dynamics of a biological neuron with dendrites can be approximated by artificial neural networks (ANN) with deep structure. However, it…
As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all…
Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…
Seismic wave arrival time measurements form the basis for numerous downstream applications. State-of-the-art approaches for phase picking use deep neural networks to annotate seismograms at each station independently, yet human experts…
This paper focuses on the feasibility of Deep Neural Operator (DeepONet) as a robust surrogate modeling method within the context of digital twin (DT) for nuclear energy systems. Through benchmarking and evaluation, this study showcases the…
Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black…
Designing effective neural networks is fundamentally important in deep multimodal learning. Most existing works focus on a single task and design neural architectures manually, which are highly task-specific and hard to generalize to…
Ensuring both feasibility and efficiency in optimal power flow (OPF) operations has become increasingly important in modern power systems with high penetrations of renewable energy and energy storage. While deep neural networks (DNNs) have…
As deep neural network (DNN) models grow ever-larger, they can achieve higher accuracy and solve more complex problems. This trend has been enabled by an increase in available compute power; however, efforts to continue to scale electronic…