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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…

Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, existing methods are insufficient to handle those PDE…

Seismic forward and inverse problems are significant research areas in geophysics. However, the time burden of traditional numerical methods hinders their applications in scenarios that require fast predictions. Machine learning-based…

The existing physical-informed Deep Operator Networks are mostly based on either the well-known mathematical formula of the system or huge amounts of data for different scenarios. However, in some cases, it is difficult to get the exact…

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein,…

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires…

DeepONet enables retraining-free inference across varying initial conditions or source terms at the cost of high computational requirements. This paper proposes a hybrid quantum operator network (Quantum AS-DeepOnet) suitable for solving 2D…

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…

Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex…

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

This paper proposes a new data-driven method for the reliable prediction of power system post-fault trajectories. The proposed method is based on the fundamentally new concept of Deep Operator Networks (DeepONets). Compared to traditional…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…

Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large…

Traditional 2D hydraulic models face significant computational challenges that limit their applications that are time-sensitive or require many model evaluations. This study presents a physics-informed Deep Operator Network (DeepONet)…

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…

Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

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…

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,…