Related papers: Novel DeepONet architecture to predict stresses in…

Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data. This property becomes especially relevant in real-world scenarios where…

Many modern datasets mix points, edges, regions, groups, objects, events, hyperedges, and relations. Yet neural architectures often force such data into grids, graphs, or sequences, obscuring higher-order structure and making…

Multi-scale features are essential for dense prediction tasks, such as object detection, instance segmentation, and semantic segmentation. The prevailing methods usually utilize a classification backbone to extract multi-scale features and…

In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

Deep Operator Network (DeepONet) is a neural network framework for learning nonlinear operators such as those from ordinary differential equations (ODEs) describing complex systems. Multiple-input deep neural operators (MIONet) extended…

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. For small Debye lengths, very steep boundary layers are developed, but standard…

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…

Deep neural networks have been one of the dominant machine learning approaches in recent years. Several new network structures are proposed and have better performance than the traditional feedforward neural network structure.…

This paper designs surrogate models with uncertainty quantification capabilities to improve the thermal performance of rib-turbulated internal cooling channels effectively. To construct the surrogate, we use the deep operator network…

Training deep learning models, particularly Transformer-based architectures such as Large Language Models (LLMs), demands substantial computational resources and extended training periods. While optimal configuration and infrastructure…

Deep neural networks have demonstrated state-of-the-art performance in a variety of real-world applications. In order to obtain performance gains, these networks have grown larger and deeper, containing millions or even billions of…

A fundamental issue in multiscale materials modeling and design is the consideration of traction-separation behavior at the interface. By enriching the deep material network (DMN) with cohesive layers, the paper presents a novel data-driven…

In this paper, we present a novel deep learning approach, deeply-fused nets. The central idea of our approach is deep fusion, i.e., combine the intermediate representations of base networks, where the fused output serves as the input of the…

Deep learning using multi-layer neural networks (NNs) architecture manifests superb power in modern machine learning systems. The trained Deep Neural Networks (DNNs) are typically large. The question we would like to address is whether it…

A universal interatomic potential for an arbitrary set of chemical elements is urgently needed in computational materials science. Graph convolution neural network (GCN) has rich expressive power, but previously was mainly employed to…

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 $u\in C(K_1)$…

Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…