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The present study investigates the accurate inference of Reynolds-averaged Navier-Stokes solutions for the compressible flow over aerofoils in two dimensions with a deep neural network. Our approach yields networks that learn to generate…

Fluid Dynamics · Physics 2022-11-17 Li-Wei Chen , Nils Thuerey

Numerical simulation for climate modeling resolving all important scales is a computationally taxing process. Therefore, to circumvent this issue a low resolution simulation is performed, which is subsequently corrected for bias using…

Atmospheric and Oceanic Physics · Physics 2023-02-08 Aniruddha Bora , Khemraj Shukla , Shixuan Zhang , Bryce Harrop , Ruby Leung , George Em Karniadakis

Wave setup plays a significant role in transferring wave-induced energy to currents and causing an increase in water elevation. This excess momentum flux, known as radiation stress, motivates the coupling of circulation models with wave…

Computational Physics · Physics 2026-04-09 Shukai Cai , Sourav Dutta , Mark Loveland , Eirik Valseth , Peter Rivera-Casillas , Corey Trahan , Clint Dawson

Hemodynamic quantities are valuable biomedical risk factors for cardiovascular pathology such as atherosclerosis. Non-invasive, in-vivo measurement of these quantities can only be performed using a select number of modalities that are not…

Quantitative Methods · Quantitative Biology 2026-02-23 Julian Suk , Dieuwertje Alblas , Barbara A. Hutten , Albert Wiegman , Christoph Brune , Pim van Ooij , Jelmer M. Wolterink

In this paper, prediction of airfoil shape from targeted pressure distribution (suction and pressure sides) and vice versa is demonstrated using both Convolutional Neural Networks (CNNs) and Deep Neural Networks (DNNs) techniques. The…

Machine Learning · Computer Science 2025-04-01 Anantram Patel , Nikhil Mogre , Mandar Mane , Jayavardhan Reddy Enumula , Vijay Kumar Sutrakar

We demonstrate how deep convolutional neural networks can be trained to predict 2+1 D hydrodynamic simulation results for flow coefficients, mean-transverse-momentum and charged particle multiplicity from the initial energy density profile.…

High Energy Physics - Phenomenology · Physics 2024-04-04 H. Hirvonen , K. J. Eskola , H. Niemi

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…

Machine Learning · Computer Science 2025-12-24 Marco A. Iglesias , Michael. E. Causon , Mikhail Y. Matveev , Andreas Endruweit , Michael . V. Tretyakov

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…

Computational Physics · Physics 2021-06-02 Christopher J Arthurs , Andrew P King

A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under…

Computational Engineering, Finance, and Science · Computer Science 2023-08-01 Junyan He , Seid Koric , Shashank Kushwaha , Jaewan Park , Diab Abueidda , Iwona Jasiuk

This paper designs surrogate models with uncertainty quantification capabilities to improve the thermal performance of rib-turbulated internal cooling channels effectively. To construct the surrogate, we use the deep operator network…

Fluid Dynamics · Physics 2023-06-15 Izzet Sahin , Christian Moya , Amirhossein Mollaali , Guang Lin , Guillermo Paniagua

The typical size of computational meshes needed for realistic geometries and high-speed flow conditions makes Computational Fluid Dynamics (CFD) impractical for full-mission performance prediction and control. Reduced-Order Models (ROMs) in…

Fluid Dynamics · Physics 2023-06-09 Haitz Sáez de Ocáriz Borde , Pietro Innocenzi , Flavio Savarino

Despite the plethora of deep learning frameworks for flow field prediction, most of them deal with flow fields on regular domains, and although the best ones can cope with irregular domains, they mostly rely on graph networks, so that real…

Machine Learning · Computer Science 2024-08-14 Laurent de Vito , Nils Pinnau , Simone Dey

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

Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…

Machine Learning · Computer Science 2024-04-30 Kazuma Kobayashi , James Daniell , Syed Bahauddin Alam

The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…

The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid…

Computational Engineering, Finance, and Science · Computer Science 2022-05-26 Sam Jacob Jacob , Markus Mrosek , Carsten Othmer , Harald Köstler

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

Computational Physics · Physics 2022-03-23 Lu Lu , Xuhui Meng , Shengze Cai , Zhiping Mao , Somdatta Goswami , Zhongqiang Zhang , George Em Karniadakis

Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost…

Materials Science · Physics 2022-07-01 Vivek Oommen , Khemraj Shukla , Somdatta Goswami , Remi Dingreville , George Em Karniadakis

Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…

Machine Learning · Computer Science 2023-04-18 Katiana Kontolati , Somdatta Goswami , George Em Karniadakis , Michael D. Shields

A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures,…

Machine Learning · Computer Science 2020-05-20 Meng Tang , Yimin Liu , Louis J. Durlofsky