Related papers: FB-HyDON: Parameter-Efficient Physics-Informed Ope…

Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…

Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-informed Adaptive-Scale Deep Operator Network for learning…

This article explores operator learning models that can deduce solutions to partial differential equations (PDEs) on arbitrary domains without requiring retraining. We introduce two innovative models rooted in boundary integral equations…

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…

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator…

Simulation and optimization are crucial for advancing the engineering design of complex systems and processes. Traditional optimization methods require substantial computational time and effort due to their reliance on resource-intensive…

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…

Full waveform inversion (FWI) infers the subsurface structure information from seismic waveform data by solving a non-convex optimization problem. Data-driven FWI has been increasingly studied with various neural network architectures to…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

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…

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…

Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an…

Phase-field simulations provide mechanistic descriptions of microstructure evolution, but repeated high-fidelity integration over long horizons and broad parameter spaces remains computationally expensive. We present PFNet, a…

This study presents an enhanced multi-fidelity Deep Operator Network (DeepONet) framework for efficient spatio-temporal flow field prediction when high-fidelity data is scarce. Key innovations include: a merge network replacing traditional…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…