Related papers: Operator learning for predicting multiscale bubble…

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,…

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)…

This study develops and validates neural network frameworks with physics-based constraints for surrogate modeling of rarefied gas dynamics across different levels of complexity. As a baseline, we first examine the BGK kinetic relaxation…

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…

Sophisticated multilayer neural networks have achieved state of the art results on multiple supervised tasks. However, successful applications of such multilayer networks to control have so far been limited largely to the perception portion…

Deep Neural Networks (DNNs) have emerged as the core enabler of many major applications on mobile devices. To achieve high accuracy, DNN models have become increasingly deep with hundreds or even thousands of operator layers, leading to…

Deep neural networks that approximate nonlinear function-to-function mappings, i.e., operators, which are called DeepONet, have been demonstrated in recent articles to be capable of encoding entire PDE control methodologies, such as…

Deep neural networks (DNNs) have successfully been applied in many fields in the past decades. However, the increasing number of multiply-and-accumulate (MAC) operations in DNNs prevents their application in resource-constrained and…

Many techniques have been developed, such as model compression, to make Deep Neural Networks (DNNs) inference more efficiently. Nevertheless, DNNs still lack excellent run-time dynamic inference capability to enable users trade-off accuracy…

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving direct current optimal power flow (DC-OPF) problems. DeepOPF is inspired by the observation that solving DC-OPF for a given power network is equivalent to characterizing…

Data-driven, deep-learning modeling frameworks have been recently developed for forecasting time series data. Such machine learning models may be useful in multiple domains including the atmospheric and oceanic ones, and in general, the…

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these…

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…

Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…

This paper integrates deep neural networks (DNNs) into structural economic models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic structure and machine learning are complements in empirical…

High percentage penetrations of renewable energy generations introduce significant uncertainty into power systems. It requires grid operators to solve alternative current optimal power flow (AC-OPF) problems more frequently for economical…

Hyperparameters searches are computationally expensive. This paper studies some general choices of hyperparameters and training methods specifically for operator learning. It considers the architectures DeepONets, Fourier neural operators…

Performance of deep learning models is strongly governed by architectural capacity, with width and depth as primary controls. However, in physical-science applications, models are often compared at a single fixed size or by separating…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…