Related papers: When Network Architecture Meets Physics: Deep Oper…

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…

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…

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…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

Thermal plasma properties play a critical role in plasma simulations and plasma-related applications. However, their strong nonlinear dependence on temperature, pressure, and gas composition makes accurate and efficient evaluation…

Multiphysics simulations play an essential role in accurately modeling complex interactions across diverse scientific and engineering domains Although neural operators especially the Fourier Neural Operator FNO have significantly improved…

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…

Time dependent reliability analysis and uncertainty quantification of structural system subjected to stochastic forcing function is a challenging endeavour as it necessitates considerable computational time. We investigate the efficacy of…

Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of…

While improvements in deep learning architectures have played a crucial role in improving the state of supervised and unsupervised learning in computer vision and natural language processing, neural network architecture choices for…

Neural operators are capable of capturing nonlinear mappings between infinite-dimensional functional spaces, offering a data-driven approach to modeling complex functional relationships in classical density functional theory (cDFT). In this…

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…

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…

Neural operators have emerged as fast surrogate models for physics simulations, yet they remain acutely vulnerable to adversarial perturbations, a critical liability for safety-critical digital twin deployments. We present a synergistic…

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators…

Neural networks are universal approximators that traditionally have been used to learn a map between function inputs and outputs. However, recent research has demonstrated that deep neural networks can be used to approximate operators,…

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…

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…

Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for…