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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…
Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent…
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…
In this paper, we investigate the applications of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate 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…
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…
We propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed operator-learning Networks (Morephy-Net) to solve parametric partial differential equations (PDEs) in noisy data regimes, for both forward…
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…
Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution…
Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…
Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…
Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the "vanilla" DeepONet is valued…
In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…
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…
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 recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations. Despite their promising…
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…
Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient. In particular, the temperature parameter controlling the noise level gives rise to a…
Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…
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…