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Operator learning is a recently developed generalization of regression to mappings between functions. It promises to drastically reduce expensive numerical integration of PDEs to fast evaluations of mappings between functional states of a…

Machine Learning · Computer Science 2025-12-23 Tian Yu Yen , Reese E. Jones , Ravi G. Patel

This work presents an online learning-based control method for improved trajectory tracking of unmanned aerial vehicles using both deep learning and expert knowledge. The proposed method does not require the exact model of the system to be…

Robotics · Computer Science 2019-05-28 Andriy Sarabakha , Erdal Kayacan

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

Machine Learning · Computer Science 2021-03-23 Sifan Wang , Hanwen Wang , Paris Perdikaris

This study aims to comprehensively investigate the deep ensemble approach, an approximate Bayesian inference, in the multi-output regression task for predicting the aerodynamic performance of a missile configuration. To this end, the effect…

Machine Learning · Computer Science 2023-11-27 Sunwoong Yang , Kwanjung Yee

Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to…

Machine Learning · Computer Science 2025-12-16 Wenchong He , Zhe Jiang , Tingsong Xiao , Zelin Xu , Yukun Li

We propose a novel framework for uncertainty quantification via information bottleneck (IB-UQ) for scientific machine learning tasks, including deep neural network (DNN) regression and neural operator learning (DeepONet). Specifically, we…

Numerical Analysis · Mathematics 2023-05-31 Ling Guo , Hao Wu , Wenwen Zhou , Yan Wang , Tao Zhou

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…

Numerical Analysis · Mathematics 2023-11-22 Amanda A. Howard , Mauro Perego , George E. Karniadakis , Panos Stinis

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While…

Machine Learning · Computer Science 2023-04-12 Hanjing Wang , Dhiraj Joshi , Shiqiang Wang , Qiang Ji

We develop a data-driven deep neural operator framework to approximate multiple output states for a diesel engine and generate real-time predictions with reasonable accuracy. As emission norms become more stringent, the need for fast and…

Signal Processing · Electrical Eng. & Systems 2025-01-16 Varun Kumar , Somdatta Goswami , Daniel J. Smith , George Em Karniadakis

Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations, potentially accelerating multi-query tasks such as design optimization and uncertainty quantification by…

Machine Learning · Computer Science 2026-02-26 Alexander Heinlein , Johannes Taraz

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

Machine Learning · Computer Science 2026-05-04 Purav Matlia , Christian Moya , Guang Lin

In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and…

Machine Learning · Computer Science 2024-03-07 Andrew Pensoneault , Xueyu Zhu

Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects…

Machine Learning · Statistics 2023-11-13 Ziyi Huang , Henry Lam , Haofeng Zhang

We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal…

Computational Engineering, Finance, and Science · Computer Science 2026-04-10 Sumanta Roy , Stephen T. Castonguay , Pratanu Roy , Michael D. Shields

Deep neural networks (DNNs) have achieved state-of-the-art performances in many important domains, including medical diagnosis, security, and autonomous driving. In these domains where safety is highly critical, an erroneous decision can…

Machine Learning · Computer Science 2019-06-12 Aryan Mobiny , Hien V. Nguyen , Supratik Moulik , Naveen Garg , Carol C. Wu

The scheduling and operation of power system becomes prominently complex and uncertain, especially with the penetration of distributed power. Load forecasting matters to the effective operation of power system. This paper proposes a novel…

Computational Engineering, Finance, and Science · Computer Science 2019-05-10 Tinghui Ouyang , Yusen He , Huajin Li , Zhiyu Sun , Stephen Baek

Deep learning for distribution grid optimization can be advocated as a promising solution for near-optimal yet timely inverter dispatch. The principle is to train a deep neural network (DNN) to predict the solutions of an optimal power flow…

Optimization and Control · Mathematics 2020-07-09 Manish K. Singh , Sarthak Gupta , Vassilis Kekatos , Guido Cavraro , Andrey Bernstein

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…

Computational Physics · Physics 2022-07-20 Lu Lu , Raphael Pestourie , Steven G. Johnson , Giuseppe Romano

The existing physical-informed Deep Operator Networks are mostly based on either the well-known mathematical formula of the system or huge amounts of data for different scenarios. However, in some cases, it is difficult to get the exact…

Signal Processing · Electrical Eng. & Systems 2026-02-24 Jieming Sun , Lichun Li

Deep neural networks have become the default choice for many of the machine learning tasks such as classification and regression. Dropout, a method commonly used to improve the convergence of deep neural networks, generates an ensemble of…

Machine Learning · Statistics 2019-04-11 Tal Kachman , Michal Moshkovitz , Michal Rosen-Zvi