Heng Xiao

Heng Xiao
Universität Stuttgart · Faculty of Aerospace Engineering and Geodesy

PhD

About

114
Publications
151,628
Reads
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4,666
Citations
Citations since 2017
71 Research Items
4466 Citations
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201720182019202020212022202302004006008001,0001,200
201720182019202020212022202302004006008001,0001,200
201720182019202020212022202302004006008001,0001,200
Introduction
Research interests: turbulence modeling, uncertainty quantification, machine learning, sediment transport
Additional affiliations
August 2020 - December 2022
Virginia Tech (Virginia Polytechnic Institute and State University)
Position
  • Professor (Associate)
January 2013 - June 2020
Virginia Tech (Virginia Polytechnic Institute and State University)
Position
  • Professor (Assistant)
November 2009 - December 2012
ETH Zürich
Position
  • PostDoc Position
Education
September 2005 - September 2009
Princeton University
Field of study
  • Civil Engineering
August 2003 - May 2005
KTH Royal Institute of Technology
Field of study
  • Scientific Computing (Computational Mathematics)
September 1999 - July 2003
Zhejiang University
Field of study
  • Civil Engineering

Publications

Publications (114)
Preprint
Full-text available
Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse problem with adjoint-based optimization, the problem can be regularized by adding additional constraints in the...
Article
Constitutive models are widely used for modeling complex systems in science and engineering, where first-principle-based, well-resolved simulations are often prohibitively expensive. For example, in fluid dynamics, constitutive models are required to describe nonlocal, unresolved physics such as turbulence and laminar–turbulent transition. However,...
Preprint
Developing robust constitutive models is fundamental and a longstanding problem for accelerating the simulation of complicated physics. Machine learning provides promising tools to construct constitutive models based on various calibration data. In this work, we propose a new approach to emulate constitutive tensor transport equations for tensorial...
Article
Full-text available
[ACCEPTED FOR PUBLICATION IN Journal of Fluid Mechanics] Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure models continue to play important roles in industrial flow simulations. However, the commonly used linear eddy viscosity models are intrinsically unable to handle flows with non-equilibrium turbulence (e.g., flows wit...
Article
Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based empirical formulas based on integral quantities such as the shape factor of the boundary layer. However, in m...
Article
Full-text available
Developing urban land surface models for modeling cities at high resolutions needs to better account for the city‐specific multi‐scale land surface heterogeneities at a reasonable computational cost. We propose using an encoder‐decoder convolutional neural network to develop a computationally efficient model for predicting the mean velocity field d...
Article
In fluid dynamics, constitutive models are often used to describe the unresolved turbulence and to close the Reynolds averaged Navier–Stokes (RANS) equations. Traditional PDE-based constitutive models are usually too rigid to calibrate with a large set of high-fidelity data. Moreover, commonly used turbulence models are based on the weak equilibriu...
Article
In this work, we propose using an ensemble Kalman method to learn a nonlinear eddy viscosity model, represented as a tensor basis neural network, from velocity data. Data-driven turbulence models have emerged as a promising alternative to traditional models for providing closure mapping from the mean velocities to Reynolds stresses. Most data-drive...
Article
Direct pore-scale simulations of fluid flow through porous media are computationally expensive to perform for realistic systems. Previous works have demonstrated using the geometry of the microstructure of porous media to predict the velocity fields therein based on neural networks. However, such trained neural networks do not perform well for unse...
Preprint
Full-text available
Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities. Such quantities include turbulent kinetic energy for eddy viscosity models and the Reynolds stress tensor (or its anisotropy) in differential stress models. However, such mod...
Preprint
Full-text available
In this work, we propose using an ensemble Kalman method to learn a nonlinear eddy viscosity model, represented as a tensor basis neural network, from velocity data. Data-driven turbulence models have emerged as a promising alternative to traditional models for providing closure mapping from the mean velocities to Reynolds stresses. Most data-drive...
Preprint
Full-text available
Partial differential equations (PDEs) play a dominant role in the mathematical modeling of many complex dynamical processes. Solving these PDEs often requires prohibitively high computational costs, especially when multiple evaluations must be made for different parameters or conditions. After training, neural operators can provide PDEs solutions s...
Article
The Reynolds-averaged Navier–Stokes (RANS)-based method is a practical tool to provide rapid assessment of jet noise-reduction concepts. However, the RANS-based method requires modeling assumptions to represent noise generation and propagation, which often reduces the predictive accuracy due to the model-form uncertainties. In this work, the ensemb...
Article
This paper introduces an ensemble-based field inversion framework to augment the turbulence models by incorporating prior physical knowledge. Different types of prior knowledge such as smoothness, prior values, and sparsity are enforced to improve the inference of the eddy viscosity and laminar–turbulent intermittency. This work first assesses the...
Article
In the last decade, the demand for stochastic engineering results has increased substantially. Concurrently, improvements in computing hardware, access to large computing clusters, and efficient statistical methods have made uncertainty quantification studies feasible for complex, computationally expensive simulations such as computational fluid dy...
Article
Constitutive and closure models play important roles in computational mechanics and computational physics in general. Classical constitutive models for solid and fluid materials are typically local, algebraic equations or flow rules describing the dependence of stress on the local strain and/or strain-rate. Closure models such as those describing R...
Article
Training data-driven turbulence models with high fidelity Reynolds stress can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based optimization, such as training deep learning models, this requires evaluating the sensitivities of the RANS equations. This paper explores the use of an e...
Preprint
Previous works have demonstrated using the geometry of the microstructure of porous media to predict the flow velocity fields therein based on neural networks. However, such schemes are purely based on geometric information without accounting for the physical constraints on the velocity fields such as that due to mass conservation. In this work, we...
Article
Full-text available
The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from in...
Article
Full-text available
Generative adversarial networks (GANs) were initially proposed to generate images by learning from a large number of samples. Recently, GANs have been used to emulate complex physical systems such as turbulent flows. However, a critical question must be answered before GANs can be considered trusted emulators for physical systems: do GANs-generated...
Preprint
Training data-driven turbulence models with high fidelity Reynolds stress can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based optimization, such as training deep learning models, this requires evaluating the sensitivities of the RANS equations. This paper explores the use of an e...
Preprint
Full-text available
The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from in...
Article
Full-text available
Machine learning (ML) provides novel and powerful ways of accurately and efficiently recognizing complex patterns, emulating nonlinear dynamics, and predicting the spatio-temporal evolution of weather and climate processes. Off-the-shelf ML models, however, do not necessarily obey the fundamental governing laws of physical systems, nor do they gene...
Article
Reconstruction of turbulent flow based on data assimilation methods is of significant importance for improving the estimation of flow characteristics by incorporating limited observations. Existing works mainly focus on using only one observation data source, e.g., velocity, wall pressure, lift or drag force, to reconstruct the flow. In practical a...
Preprint
Full-text available
Reconstruction of turbulent flow based on data assimilation methods is of significant importance for improving the estimation of flow characteristics by incorporating limited observations. Existing works mainly focus on using only one observation data source, e.g., velocity, wall pressure, lift or drag force, to reconstruct the flow. In practical a...
Preprint
Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily extended to flow configurations where the transition process depends on a large set of parameters. In comparison, neu...
Preprint
Full-text available
Constitutive models are widely used for modelling complex systems in science and engineering, where first-principle-based, well-resolved simulations are often prohibitively expensive. For example, in fluid dynamics, constitutive models are required to describe nonlocal, unresolved physics such as turbulence and laminar-turbulent transition. In part...
Article
Full-text available
Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily extended to flow configurations where the transition process depends on a large set of parameters. In comparison, neu...
Preprint
Full-text available
In many areas of science and engineering, it is a common task to infer physical fields from sparse observations. This paper presents the DAFI code intended as a flexible framework for two broad classes of such inverse problems: data assimilation and field inversion. DAFI generalizes these diverse problems into a general formulation and solves it wi...
Preprint
Full-text available
Constitutive and closure models play important roles in computational mechanics and computational physics in general. Classical constitutive models for solid and fluid materials are typically local, algebraic equations or flow rules describing the dependence of stress on the local strain and/or strain rate. Closure models such as those describing R...
Article
Full-text available
An accurate boundary-layer transition prediction method integrated with computational fluid dynamics (CFD) solvers is pursued for hypersonic boundary-layer flows over slender hypersonic vehicles at flight conditions. The geometry and flow conditions are selected to match relevant trajectory locations from the ascent phase of the HIFiRE-1 flight exp...
Article
Inverse problems in computational mechanics consist of inferring physical fields that are latent in the model describing some observable fields. For instance, an inverse problem of interest is inferring the Reynolds stress field in the Navier–Stokes equations describing mean fluid velocity and pressure. The physical nature of the latent fields mean...
Preprint
Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based empirical formulas based on integral quantities such as the shape factor of the boundary layer. However, in m...
Article
Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse problem with adjoint-based optimization, the problem can be regularized by adding additional constraints in the...
Preprint
Bayesian uncertainty quantification (UQ) is of interest to industry and academia as it provides a framework for quantifying and reducing the uncertainty in computational models by incorporating available data. For systems with very high computational costs, for instance, the computational fluid dynamics (CFD) problem, the conventional, exact Bayesi...
Article
Full-text available
Bayesian uncertainty quantification (UQ) is of interest to industry and academia as it provides a framework for quantifying and reducing the uncertainty in computational models by incorporating available data. For systems with very high computational costs, for instance, the computational fluid dynamics (CFD) problem, the conventional, exact Bayesi...
Article
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 for decades. With recent advances in machine learning, data-driven turbulence models have become attractive alt...
Article
In view of the long stagnation in traditional turbulence modeling, researchers have attempted using machine learning to augment turbulence models. This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning. We also discuss our works on ensemble-based field inversion to provi...
Article
Simulating complex physical systems often involves solving partial differential equations (PDEs) with some closures due to the presence of multi-scale physics that cannot be fully resolved. Although the advancement of high performance computing has made resolving small-scale physics possible, such simulations are still very expensive. Therefore, re...
Preprint
Full-text available
Generative adversarial networks (GANs) are initially proposed to generate images by learning from a large number of samples. Recently, GANs have been used to emulate complex physical systems such as turbulent flows. However, a critical question must be answered before GANs can be considered trusted emulators for physical systems: do GANs-generated...
Preprint
Full-text available
Inverse problems in computational mechanics consist of inferring physical fields that are latent in the model describing some observable fields. For instance, an inverse problem of interest is inferring the Reynolds stress field in the Navier--Stokes equations describing mean fluid velocity and pressure. The physical nature of the latent fields mea...
Preprint
Full-text available
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 for decades. With recent advances in machine learning, data-driven turbulence models have become attractive al...
Article
In uncertainty quantification of computational models (e.g., turbulence modeling) with Bayesian inferences, Gaussian processes are commonly used as the prior for model discrepancies. However, constructing the covariance kernel is a challenging task that requires significant physical knowledge of the problem. On the other hand, often the model discr...
Preprint
Full-text available
Simulating complex physical systems often involves solving partial differential equations (PDEs) with some closures due to the presence of multi-scale physics that cannot be fully resolved. Therefore, reliable and accurate closure models for unresolved physics remains an important requirement for many computational physics problems, e.g., turbulenc...
Preprint
Full-text available
****PUBLISHED ONLINE in PROGRESS IN AEROSPACE SCIENCES https://doi.org/10.1016/j.paerosci.2018.10.001**** In computational fluid dynamics simulations of industrial flows, models based on the Reynolds-averaged Navier--Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major obs...
Article
In computational fluid dynamics simulations of industrial flows, models based on the Reynolds-averaged Navier–Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major obstacle for the predictive capability of RANS simulations. This review examines both the parametric and struc...
Article
Full-text available
While data-based approaches were found to be useful for subgrid scale (SGS) modeling in Reynolds-averaged Navier-Stokes (RANS) simulations, there have not been many attempts at using machine learning techniques for wall modeling in large-eddy simulations (LESs). Large-eddy simulation differs from RANS simulation in many aspects. For one thing, LES...
Article
Full-text available
Modeled Reynolds stress is a major source of model-form uncertainties in Reynolds-averaged Navier–Stokes (RANS) simulations. Recently, a physics-informed machine learning (PIML) approach has been proposed for reconstructing the discrepancies in RANS-modeled Reynolds stresses. The merits of the PIML framework have been demonstrated in several canoni...
Article
Full-text available
Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier–Stokes (RANS) equations. In the past few years, with the availability of large and diverse data sets, researchers have begun to explore methods to systematically inform tur...
Preprint
Full-text available
Modeled Reynolds stress is a major source of model-form uncertainties in Reynolds-averaged Navier-Stokes (RANS) simulations. Recently, a physics-informed machine-learning (PIML) approach has been proposed for reconstructing the discrepancies in RANS-modeled Reynolds stresses. The merits of the PIML framework has been demonstrated in several canonic...
Article
Full-text available
Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) generation of porous media samples, (2) computation of permeability via fluid dynamics simulations, (3) training of convolutional neur...
Preprint
Full-text available
Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier--Stokes (RANS) equations. In the past few years, with the availability of large and diverse datasets, researchers have begun to explore methods to systematically inform tur...
Article
Full-text available
Feature identification is an important task in many fluid dynamics applications and diverse methods have been developed for this purpose. These methods are based on a physical understanding of the underlying behavior of the flow in the vicinity of the feature. Particularly, they rely on definition of suitable criteria (i.e. point-based or neighborh...
Article
Full-text available
Reynolds-averaged Navier-Stokes (RANS) equations are widely used in engineering turbulent flow simulations. However, the mean flow fields predicted by RANS solvers could come with large discrepancies due to the uncertainties in modeled Reynolds stresses. Recently, Wang et al. demonstrated that machine learning can be used to improve the RANS modele...
Article
Full-text available
Flood hazards caused by tsunamis can cause enormous amounts of casualties and property losses. However, these hazards often occur at unexpected locations, which poses challenges for direct observations of flood source characteristics (e.g. flow speed and water depth in tsunamis-induced inundations). For this reason, inverse modelling methods based...
Article
Full-text available
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 relevance, which is largely caused by model-form uncertainties associated with the Reynolds stresses. Recentl...
Article
Full-text available
Proper quantification and propagation of uncertainties in computational simulations are of critical importance. This issue is especially challenging for computational fluid dynamics (CFD) applications. A particular obstacle for uncertainty quantifications in CFD problems is the large model discrepancies associated with the CFD models used for uncer...
Article
Full-text available
Although Reynolds-Averaged Navier–Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing a...
Article
Full-text available
The settling of cohesive sediment is ubiquitous in aquatic environments. In the settling process, the silt particles show behaviors that are different from non-cohesive particles due to the influence of inter-particle cohesive force. While it is a consensus that cohesive behaviors depend on the characteristics of sediment particles (e.g., Bond numb...
Article
Full-text available
Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally applicable RANS models with predictive capabilities are still lacking. Recently, data-driven methods have been propose...
Article
Full-text available
Although an increased availability of computational resources has enabled high-fidelity simulations of turbulent flows, the RANS models are still the dominant tools for industrial applications. However, the predictive capabilities of RANS models are limited by potential inaccuracy driven by hypotheses in the Reynolds stress closure. Recently, a Phy...