Hello Nick,

A Bayesian surrogate modelling approach would be a good idea. Using its exploration - exploitation strategies to find the optimal parameters it will be possible to find best design. These methods allow to do simulations with theoretically optimal sampling and is necessary since each CFD simulation is expensive. Gaussian process regression is well suited for the surrogate modelling. I will be necessary to find a reduced order representation for the geometrical parameters also.

So there will be a regression between your geometrical parameters and the design parameters. The surrogate model will initially be naive and use exploratory strategies. Once the surrogate model starts to build its confidence, bias the acquisition function to find the optimal parameters based on your criteria.

Hope that helps.

Amal

Thanks heaps Amal Roy Murali! I assume you applied this to aerospace design? How did the Bayesian model perform (e.g. did you compare it's results to CFD, or experimental, results)?

Machine learning–accelerated computational fluid dynamics

PNAS

https://www.pnas.org › doi › pnas.2101784118

by D Kochkov · 2021 · Cited by 719 — Accurate simulation of fluids is important for many science and engineering problems but is very computationally demanding.

Emerging trends in machine learning for

computational fluid dynamics

Ricardo Vinuesa1,2 and Steven L. Brunton3

1 FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden

2 Swedish e-Science Research Centre (SeRC), Stockholm, Sweden

3 Department of Mechanical Engineering, University of Washington, Seattle,WA 98195, United States

Abstract

The renewed interest from the scientific community in machine learning (ML) is opening many new areas of

research. Here we focus on trends in ML that are providing opportunities to advance the field of computational

fluid dynamics (CFD). We discuss synergies between ML and CFD that have already shown benefits, and we also

assess areas that are under development and may produce important benefits in the coming years. We believe that

it is also important to emphasize a balanced perspective of cautious optimism for these emerging approaches.

Keywords: machine learning (ML); deep learning (DL); artificial intelligence (AI); computational fluid dynamics

(CFD); direct numerical simulation (DNS); large-eddy simulation (LES); Reynolds-averagedNavier–Stokes (RANS);

reduced-ordermodel (ROM)

Introduction

Machine learning (ML) is a rapidly developing field of research that has transformed the state-of-the-art capabilities

for many traditional tasks in computer science, such as image classification and captioning, natural language processing,

and recommender systems. The numerous success stories of ML have led to widespread adoption in the

scientific and engineering communities as well, fueled by a growing wealth of data, computing resources, and advanced

optimization algorithms. This is especially true in the field of fluidmechanics, where emerging technologies

complement existing computational and experimental methods, providing a unified approach to building models

from data [5].

Despite these advancements, there remains a gap in understanding how ML can be best integrated with computational

fluid dynamics (CFD). This paper aims to explore the synergies between ML and CFD, showcasing the

potential benefits and challenges in combining these fields. ML can advance CFD in areas such as turbulence modeling,

development of inflow boundary conditions, subgrid-scalemodels for large-eddy simulations (LES), closures

for Reynolds-averaged Navier–Stokes (RANS) equations, development of reduced-ordermodels (ROMs), and flow

control [29]. Our approach is to first examine established techniques, such as proper-orthogonal decomposition

(POD) and dynamic-mode decomposition (DMD), alongside deep-learning techniques with autoencoders. Next,

we delve into emerging opportunities where ML and CFD can be further integrated, highlighting ongoing challenges

and potential solutions. We conclude by summarizing the insights gained and potential future directions for

this interdisciplinary research.

Overview of applications

Some of the more relevant applications at the intersection of ML and CFD include the following:

• Modeling the near-wall region of wall-bounded turbulence. Milano and Koumoutsakos [18] developed,

20 years ago, a method to predict the relevant features of turbulent channel flow close to the wall by using

deep neural networks. In addition to the interest of this work from the perspective of modeling turbulence,

and potentially developing wall models, the authors also established connections between neural networks

and traditional methods such as proper-orthogonal decomposition (POD). In particular, they showed that by

restricting the neural networkmodel to be linear, the network essentially learns the features produced by standard

POD. This topic has received renewed attention in recent years due to the possibility of training deeper

neural network models with larger data sets, as well as the emergence of novel learning architectures [2].

 Corresponding author: Ricardo Vinuesa ([email protected])

1

• Development of inflow conditions for turbulence simulations. This is a critical area for CFD when it

comes to achieving high-Reynolds-number (Re) conditions and simulating complex geometries. Spatiallydeveloping

turbulent boundary layers (TBLs) require very long domains to reach high Reynolds numbers,

and if part of the low-Re region can be replaced by an adequate inflow condition, simulations at the relevant

high-Re regime can become feasible. Similarly, if a simulation is designed to study the turbulent flow around

a complex array of obstacles, it is beneficial to replace the inflow section of the simulation by a suitable inflow

condition, thus yielding significant computational savings. Traditional approaches to these inflows have

relied on various filters, recycling approaches, and imposing synthetic turbulent structures. However, recent

progress in ML has enabled the use of deep-learning approaches to produce robust inflow conditions,

including the use of modern architectures, such as transformers [32].

• Development of boundary conditions for external-flowsimulations. One of the challenges of simulating external

flows, e.g. the flow past an airfoil, is the need for large computational domains to adequately reproduce

the far-field conditions and the pressure distribution around the wing. While the resolution of the portion

of the domain near the far field is often already quite coarse, being able to replace this region entirely by a

suitable boundary condition would lead to significant computational savings. Furthermore, it is important to

be able to establish prescribed pressure-gradient (PG) conditions so as to study PG TBLs and their non-trivial

flow-history effects. To this end, a number of ML approaches have been recently developed for effective

boundary-condition design [2]. In particular, Gaussian-process regression has been successfully employed to

optimize the shape of the domain to prescribe a particular PG distribution.

• Improved subgrid-scale (SGS) models for large-eddy simulations (LESs). In this application, the goal is

to develop frameworks to supplement coarse numerical simulations, where only the largest turbulent scales

are resolved, with additional information corresponding to the flow scales

Hello Nick, Yes, for my interests, Gaussian process based surrogate is quite satisfactory.

Thanks Suresh Ahuja! I should be able to get access to official literature, so links/names to/of article will suffice.

On computation effort, Amal Roy Murali, I was able to relax the mesh using cfMesh pretty effectively. This, in combination with using OpenFOAM's solvers that allow running computations with CourantNumbers > 1 means I can hugely reduce my simulation times.

Hi Nick Howlett, we used DoE-based internal combustion engine piston geometry design generation, ran CFD simulations to understand the ICE performance and emissions for each geometry, and then used ML to train the models on the empirical correlations between the piston geometry parameters and ICE performance and emissions. Used the ML models to further optimize the piston geometry to maximize performance and minimize emissions further. We used CAESES to generate different piston shapes based on the SOBOL sequence and Converge CFD solver. The ML framework used a SuperLearner approach developed in-house using Python and R languages. We further co-optimized the effect of boundary and initial conditions along with geometry. For more details, refer to our works

(PDF) Co-optimization of piston bowl and injector for light-duty GCI engine using CFD and ML (researchgate.net)

(PDF) DoE-ML guided optimization of an active pre-chamber geometry using CFD (researchgate.net)

(PDF) Machine Learning and Response Surface-Based Numerical Optimization of the Combustion System for a Heavy-Duty Gasoline Compression Ignition Engine (researchgate.net)