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

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…

In machine learning, there is a fundamental trade-off between ease of optimization and expressive power. Neural Networks, in particular, have enormous expressive power and yet are notoriously challenging to train. The nature of that…

Failure trajectories, identifying the probable failure zones, and damage statistics are some of the key quantities of relevance in brittle fracture applications. High-fidelity numerical solvers that reliably estimate these relevant…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

Deep Neural Networks (DNNs) are becoming an important tool in modern computing applications. Accelerating their training is a major challenge and techniques range from distributed algorithms to low-level circuit design. In this survey, we…

We describe N-body networks, a neural network architecture for learning the behavior and properties of complex many body physical systems. Our specific application is to learn atomic potential energy surfaces for use in molecular dynamics…

Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering…

The goal of this work is to investigate the capability of a neural operator (DeepONet) to accurately capture the complex deformation of a platelet's membrane under shear flow. The surrogate model approximated by the neural operator predicts…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Thermal analysis is crucial in 3D-IC design due to increased power density and complex heat dissipation paths. Although operator learning frameworks such as DeepOHeat~\cite{liu2023deepoheat} have demonstrated promising preliminary results…

In the last decade, deep learning has become a major component of artificial intelligence. The workhorse of deep learning is the optimization of loss functions by stochastic gradient descent (SGD). Traditionally in deep learning, neural…

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…

Our theoretical understanding of deep learning has not kept pace with its empirical success. While network architecture is known to be critical, we do not yet understand its effect on learned representations and network behavior, or how…

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…

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires…

Deep Material Network (DMN) has recently emerged as a data-driven surrogate model for heterogeneous materials. Given a particular microstructural morphology, the effective linear and nonlinear behaviors can be successfully approximated by…

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)…

Deep learning yields great results across many fields, from speech recognition, image classification, to translation. But for each problem, getting a deep model to work well involves research into the architecture and a long period of…

In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…

Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…