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Turbulence is ubiquitous in engineering and science, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide savings exceeding ten orders of magnitude but introduce unclosed terms (the…

Fluid Dynamics · Physics 2026-05-27 Daniel Dehtyriov , Jonathan F. MacArt , Justin Sirignano

Current modeling approaches for hydrological modeling often rely on either physics-based or data-science methods, including Machine Learning (ML) algorithms. While physics-based models tend to rigid structure resulting in unrealistic…

Machine Learning · Statistics 2021-04-23 Pravin Bhasme , Jenil Vagadiya , Udit Bhatia

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize…

Fluid Dynamics · Physics 2023-01-24 Hongwei Tang , Yan Wang , Tongguang Wang , Linlin Tian

Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In…

Machine Learning · Computer Science 2025-12-16 Han Wan , Qi Wang , Yuan Mi , Rui Zhang , Hao Sun

Model extrapolation to unseen flow is one of the biggest challenges facing data-driven turbulence modeling, especially for models with high dimensional inputs that involve many flow features. In this study we review previous efforts on…

Fluid Dynamics · Physics 2020-01-16 Shirui Luo , Jiahuan Cui , Madhu Vellakal , Jian Liu , Enyi Jiang , Seid Koric , Volodymyr Kindratenko

Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier-Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning algorithms have opened up a…

Fluid Dynamics · Physics 2019-02-05 Nicholas Geneva , Nicholas Zabaras

Physics-informed neural networks (PINNs) have recently emerged as a promising alternative for extracting unknown quantities from experimental data. Despite this potential, much of the recent literature has relied on sparse, high-fidelity…

Fluid Dynamics · Physics 2026-01-09 Christian Toma , Bharathram Ganapathisubramani , Sean Symon

Computational fluid dynamics models based on Reynolds-averaged Navier--Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant…

Fluid Dynamics · Physics 2019-10-04 Heng Xiao , Jin-Long Wu , Sylvain Laizet , Lian Duan

Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression…

Machine Learning · Statistics 2025-07-15 Nathan Doumèche

Accurate and robust models for the pressure strain correlation are an essential component for the success of Reynolds Stress Models in turbulent flow simulations. However replicating the non-local action of pressure using only local tensors…

Fluid Dynamics · Physics 2019-03-14 Jyoti Prakash Panda

This paper presents a new approach to simulate forward and inverse problems of moving loads using physics-informed machine learning (PIML). Physics-informed neural networks (PINNs) utilize the underlying physics of moving load problems and…

Machine Learning · Computer Science 2023-04-04 Taniya Kapoor , Hongrui Wang , Alfredo Núñez , Rolf Dollevoet

This work determines the inaccuracy of using Reynolds averaged Navier Stokes (RANS) turbulence models in transition to turbulent flow regimes by predicting the model-based discrepancies between RANS and large eddy simulation (LES) models…

Fluid Dynamics · Physics 2019-01-21 Mustafa Usta , Ali Tosyali

Turbulence modeling is a classical approach to address the multiscale nature of fluid turbulence. Instead of resolving all scales of motion, which is currently mathematically and numerically intractable, reduced models that capture the…

Fluid Dynamics · Physics 2018-12-10 Rui Fang , David Sondak , Pavlos Protopapas , Sauro Succi

Physics-Informed Machine Learning (PIML) has gained momentum in the last 5 years with scientists and researchers aiming to utilize the benefits afforded by advances in machine learning, particularly in deep learning. With large scientific…

Computational Physics · Physics 2021-05-26 Samuel J. Raymond , David B. Camarillo

This paper is aimed at using the newly developing field of physics informed machine learning (PIML) to develop models for predicting the remaining useful lifetime (RUL) aircraft engines. We consider the well-known benchmark NASA Commercial…

Machine Learning · Computer Science 2024-06-25 Sriram Nagaraj , Truman Hickok

We present a data-driven framework for turbulence modeling, applied to flow prediction in the FDA nozzle. In this study, the standard RANS equations have been modified using an implicit-explicit hybrid approach. New variables were…

Fluid Dynamics · Physics 2025-10-02 Hossein Geshani , Mehrdad Raisee Dehkordi , Masoud Shariat Panahi

Data-driven turbulence modeling is a newly emerged research area in thermal hydraulics simulation of nuclear power plant (NPP). The most common CFD method used in NPP thermal hydraulics simulation is Reynolds-averaged Navier-Stokes (RANS)…

Fluid Dynamics · Physics 2020-05-04 Yangmo Zhu , Nam Dinh

Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the…

Machine Learning · Computer Science 2023-08-14 Shinjan Ghosh , Amit Chakraborty , Georgia Olympia Brikis , Biswadip Dey

Numerical simulations based on Reynolds-Averaged Navier--Stokes (RANS) equations are widely used in engineering design and analysis involving turbulent flows. However, RANS simulations are known to be unreliable in many flows of engineering…

Fluid Dynamics · Physics 2017-09-19 Jinlong Wu , Rui Sun , Sylvain Laizet , Heng Xiao

The design of film cooling systems relies heavily on Reynolds-Averaged Navier-Stokes (RANS) simulations, which solve for mean quantities and model all turbulent scales. Most turbulent heat flux models, which are based on isotropic diffusion…

Fluid Dynamics · Physics 2019-10-09 Pedro M. Milani , Julia Ling , John K. Eaton