Related papers: In-Context Multi-Operator Learning with DeepOSets

Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant computational…

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

The Deep Operator Network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models…

In this paper, we consider the use of deep neural networks in the context of Multiple-Input-Multiple-Output (MIMO) detection. We give a brief introduction to deep learning and propose a modern neural network architecture suitable for this…

Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contemporary neural operators designed to approximate general maps…

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…

Scaling model capacity has been vital in the success of deep learning. For a typical network, necessary compute resources and training time grow dramatically with model size. Conditional computation is a promising way to increase the number…

We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a…

With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

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…

We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After…

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of…

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,…

We propose a Deep Operator Network~(DeepONet) framework to learn the dynamic response of continuous-time nonlinear control systems from data. To this end, we first construct and train a DeepONet that approximates the control system's local…

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…