Related papers: Operator Learning for Consolidation: An Architectu…
We present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two sub-networks, namely the branch and trunk networks. Typically, the two…
Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…
Most neural-operator surrogates for PDEs inherit from DeepONet-style formulations the requirement that the input function be sampled at a fixed, ordered set of sensors. This assumption limits applicability to problems with variable sensor…
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…
Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…
FNO and DeepONet are by far the most popular neural operator learning algorithms. FNO seems to enjoy an edge in popularity due to its ease of use, especially with high dimensional data. However, a lesser-acknowledged feature of DeepONet is…
Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on…
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…
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…
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)…
In this work, we introduce a novel neural operator, the Solute Transport Operator Network (STONet), to efficiently model contaminant transport in micro-cracked porous media. STONet's model architecture is specifically designed for this…
This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…
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…
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 novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…
Shape optimization is essential in aerospace vehicle design, including reentry systems, and propulsion system components, as it directly influences aerodynamic efficiency, structural integrity, and overall mission success. Rapid and…
Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…
Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…
This paper designs an Operator Learning framework to approximate the dynamic response of synchronous generators. One can use such a framework to (i) design a neural-based generator model that can interact with a numerical simulator of the…
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…