Related papers: Structure-Preserving Operator Learning: Modeling t…
An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…
Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either…
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…
Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…
Kinetic simulations excel at capturing microscale plasma physics phenomena with high accuracy, but their computational demands make them impractical for modeling large-scale space and astrophysical systems. In this context, we build a…
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 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…
Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…
This paper focuses on the feasibility of Deep Neural Operator (DeepONet) as a robust surrogate modeling method within the context of digital twin (DT) for nuclear energy systems. Through benchmarking and evaluation, this study showcases the…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…
Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…