Related papers: Topological DeepONets and a generalization of the …
Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…
In this paper, we propose a DeepONet structure with causality to represent the causal linear operators between Banach spaces of time-dependent signals. The theorem of universal approximations to nonlinear operators proposed in…
Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…
The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\mathbb{X}$ embedded…
Deep operator networks (DeepONets) are trained to predict the linear amplification of instability waves in high-speed boundary layers and to perform data assimilation. In contrast to traditional networks that approximate functions,…
Deep Operator Networks (DeepONets) have become a central tool in data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk design based…
Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…
A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under…
The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…
We study shallow and deep neural networks whose inputs range over a general topological space. The model is built from a prescribed family of continuous feature maps and reduces to multilayer feedforward networks in the Euclidean case. We…
Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…
We establish universality and expression rate bounds for a class of neural Deep Operator Networks (DON) emulating Lipschitz (or H\"older) continuous maps $\mathcal G:\mathcal X\to\mathcal Y$ between (subsets of) separable Hilbert spaces…
Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…
The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…
XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we show that the Cauchy activation functions used in XNet can…
We study feedforward neural networks with inputs from a topological space (TFNNs). We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this…
Deep Operator Networks (DeepONets) have emerged as a powerful surrogate modeling framework for learning solution operators in PDE-governed systems. While their use is expanding across engineering disciplines, applications in geotechnical…
In this work, we consider the non-invasive medical imaging modality of Electrical Impedance Tomography (EIT), where the goal is to recover the conductivity in a medium from boundary current-to-voltage measurements, i.e., the…
Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior…
This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…