Machine Learning to speed up Computational Fluid Dynamics engineering simulations for built environments: A review

Most CFD applications for built environments relate to comfort, health, energy efficiency, or safety [6]. They cover indoor (Fig. 1) and outdoor (Fig. 2) flows, operating at different scales. In indoor applications, the focus is on air movement within a building, considering factors such as ventilation, temperature gradients, and the presence of pollutants. Ensuring the thermal comfort of occupants and maintaining satisfactory indoor air quality (IAQ) are key priorities. In addition, anticipating smoke propagation is critical for fire risk assessment. Outdoor simulations investigate the external airflow behavior in built environments. Such analysis can yield significant insights into various aspects of urban design, including pedestrian comfort, natural ventilation potential, wind load, urban thermal environment, and pollutant dispersion. CFD tools can assist in studying all of these topics [6], [21]. In particular, CFD can accurately identify flow patterns, which has the potential to enhance building design.

Various simplified approaches are being developed and improved to produce faster flow simulations [32], [33]. For example, Xu et al. [32] mentioned the porous media model [34], [35], fast fluid dynamics [36], [37], multizone model [38], lattice Boltzmann method [39], [40], or coarse-grid CFD [41]. Regardless of the method, model simplifications inevitably reduce accuracy for some configurations. Nevertheless, when appropriately used, simplified models remain powerful approaches to achieving fast calculations and delivering valuable insights, although they cannot entirely replace traditional CFD methods. For example, Seifert et al. [42] demonstrated that the simplified macroscopic method frequently employed for wind-driven ventilation analysis can yield satisfactory results for engineering applications. However, outcomes can be dramatically inaccurate depending on building porosity and wind direction. In another context, Hodges et al. [43] emphasized that fire zone models cannot predict complex configurations and may lack the necessary resolution for hazard analysis.

Simplified models have been the subject of extensive study over the past few years. On the other hand, there has recently been a proliferation of studies on machine learning approaches that may offer a breakthrough in accelerating simulations. New turnkey ML tools are beginning to emerge, particularly for urban wind modeling [44], [45], [46]. Their objective is to revolutionize early-stage design with instantaneous predictions. However, the lack of detail provided about the performance and the ML methods used under the hood limits the ability to make a comprehensive evaluation. We believe that a review should help clarify recent advances. Thus, our study focuses on ML techniques, potentially hybridized with traditional approaches, to expedite built environment CFD simulations.

Machine learning leverages data to gain insight into the behavior of systems, opening up a range of potential applications across scientific fields [47], [48]. The ML framework is powerful in that it requires no prior knowledge of the laws of the underlying system. Furthermore, a model can generate predictions almost instantaneously once the learning phase is complete. Returning to our main topic, this advantage may be exploited to accelerate computations in fluid mechanics.

ML algorithms are traditionally divided into three categories, depending on the information available in the data and the nature of the knowledge to be extracted. (i) In supervised learning, a model is trained to predict a specific outcome directly provided by the dataset, i.e., the labels. The learning algorithm aims to minimize a loss function that quantifies the discrepancy between the model predictions and the target values over the training data (Fig. 3). (ii) In contrast, unsupervised learning extracts information from unlabeled data about the underlying probability densities using techniques such as clustering or dimensionality reduction. In particular, the latter is instrumental in machine learning for fluid mechanics [15]. An encoder–decoder scheme compresses data while retaining essential information (Fig. 4). (iii) As the name suggests, semisupervised learning bridges unsupervised and supervised methods, addressing situations where not all data are labeled. Techniques such as generative models or reinforcement learning, found in fluid dynamics applications, usually fall into this category [15]. A common feature is that these algorithms generate data to improve their own performance.

Nowadays, deep learning is undoubtedly the most popular machine learning approach [13]. In practice, deep learning architectures are based on deep neural networks, which are capable of approximating any continuous function [49], [50]. The capacity of neural networks to handle large datasets [51], [52] and their efficiency in being trained on graphics processing units (GPUs) give them a distinct advantage, contributing to their popularity. Researchers now have the means to train much deeper models than was conceivable a few decades ago [13], pushing back the limits of neural networks. A notable breakthrough is that deep learning can process raw data, avoiding the need for feature engineering to create helpful model inputs [12]. Nevertheless, it is worth remembering that even if deep learning is very efficient in a large panel of tasks, classical data-driven methods should not be discarded. Complex models also come with difficulties such as overfitting, lack of generalization, bad interpretability, and a heavy training process.

The simplest approach is to build an ML-based surrogate model to replace an entire CFD simulation. While effective in specific applications, this method tends to generalize poorly [18]. Incorporating physical knowledge to guide or constrain the ML model (see Section 3.2.2) represents a promising strategy for enhancing model performance and ensuring the generation of physically consistent predictions. That is why research efforts are shifting toward data-driven models that enforce underlying physics [19], [75].

In addition to the aforementioned methods, other initiatives indirectly reduce calculation times by targeting the simulation preprocessing steps. For example, estimating realistic boundary conditions (e.g., inflow) may reduce the size of the computational domain and affect computation time [75], [92]. Another promising avenue for acceleration is automatic mesh generation, a particularly time-consuming process requiring expert knowledge [18], [93], [94].

As stated in Section 2.2, engineers mainly rely on RANS and LES approaches. However, turbulence closure models can oversimplify the flow behavior and be difficult to tune for a specific use case. Hence, turbulence modeling is one of the major areas of research in ML-enhanced CFD [15], [16], [17], [75]. Data-driven algorithms can assist in calibrating turbulence models to a particular application, learn part of a closure term, or even provide entirely new ML-based turbulence models [95], [96]. Given the high cost of LES for wall-bounded flows, which are common in engineering, some attempts have been made to develop data-driven wall models for LES [97], [98], [99]. More generally, ML is a powerful and promising approach for all kinds of fluid flow underlying models, e.g., turbulent, reacting, or porous media flows.

ML models are not primarily designed to reduce computational time in these cases. Nevertheless, improved accuracy can broaden the scope of applicability for lower-cost simulations, such as RANS or wall-modeled LES. It should be noted that hybrid ML-CFD strategies (presented in Section 4.1) can also speed up approaches such as RANS and LES. For example, Obiols-Sales et al. [100] successfully coupled RANS steady simulations with a CNN to accelerate the convergence.

Reduced-order models (ROMs) [101] offer a low-dimensional, low-fidelity representation of complex systems. The first step is identifying an appropriate low-dimensional basis, which can be achieved through a range of dimensionality reduction techniques. Then, the objective is to capture the system dynamics expressed in the reduced basis. ROMs have the potential to decrease fluid mechanics computations up to real-time flow approximation. However, this speed-up comes at the cost of a limited scope of application. Indeed, ROMs are usually designed for a specific flow configuration and may not generalize well [75].

Proper orthogonal decomposition (POD) [102] is the most widely used technique in fluid dynamics for finding a low-dimensional orthogonal spatial basis from flow snapshots. The basis components, designated as modes, have the dimension of the studied domain. This linear method is physically interpretable, which helps improve our physical understanding of complex flows [103]. POD modes are typically ordered by energy content, and the first few modes show the main flow structures (Fig. 10). One advantage of POD is that it allows for selecting the number of modes included on a reduced basis, which adjusts the trade-off between simulation fidelity and computational speed. The Galerkin projection is a popular choice for projecting the physical governing equations onto the modes. This procedure yields a new system that can be solved faster than the full-order model. However, the process is intrusive, i.e., it requires explicit knowledge of the governing equations.

ML progress offers new opportunities for improving reduced-order modeling strategies [75]. A contemporary approach is to train a neural network to map high-dimensional flow snapshots to a low-dimensional latent space in a non-intrusive manner, using, e.g., autoencoders (AEs) [108]. Non-intrusive reduced-order models (NIROMs) can solve the main limitations of classical intrusive approaches. (i) NIROMs avoid the need for cumbersome CFD code manipulations during the projection step. (ii) They may learn a more compact data representation using non-orthogonal and nonlinear encoding. (iii) Linear methods such as POD and DMD may encounter difficulties in handling nonlinearities. Modern ML techniques can also be instrumental in capturing the system dynamics of the flow on a reduced basis. Neural networks with specific architectures, such as LSTMs, are trained to predict the nonlinear temporal evolution of a flow.

POD, DMD, and other ROMs are ideal candidates for tackling fluid flow control tasks, where model responsiveness is critical. It should also be noted that the deep reinforcement learning framework [109], which brings deep neural networks into the reinforcement learning [110] process, is also well-suited to complex control issues such as those related to fluid dynamics [111].

Westermann and Evins [112] pointed out that surrogate modeling is already a prevalent trend in current research on building performance simulation and optimization. Their literature review concentrated on using ML surrogates to improve the design of sustainable buildings. Although the conclusions drawn are relevant for CFD surrogate models, it is worth noting that almost all the listed surrogate models target building simulation software that does not include CFD codes. The authors identified four stages in the building design process that can benefit from fast surrogate models: (i) conceptual design, (ii) design optimization, (iii) sensitivity analysis, and (iv) uncertainty analysis. The review highlighted promising accelerations for building design optimization tasks, reducing computation time by up to 80% without compromising the optimum quality. However, challenges remain to be addressed, particularly regarding generalizability, interpretability, and the computational cost of creating surrogate models [20], [112].

As illustrated in Table 1, many recent studies have applied ML techniques to replace heavy built environment CFD simulations completely. We can observe that all building applications (indoor and outdoor) are part of this trend.

Reduced-order models are capable of providing predictions in near real-time for building engineering CFD studies by capturing main flow features (see Section 4.3). Masoumi-Verki et al. [137] reviewed recent advances in ROMs for predicting urban airflow and pollutant dispersion. They reported that the current focus is on NIROMs, which demonstrate superior potential for approximating real-world nonlinear wind flows. The authors also noted that the POD technique may not be the best choice for urban flow due to constantly changing boundary conditions, which can deteriorate POD performance.

The classical POD approach has been extensively studied for modeling built environments but remains a standard for reducing dimensionality [137]. Lattimer et al. [104] demonstrated, in a simple 2D case (see Fig. 10), that POD can reasonably represent the global buoyant plume flow 2–3 orders of magnitude faster than CFD simulations. By combining POD with radial basis function (RBF) interpolation, Luo et al. [24] successfully obtained accurate and rapid predictions of indoor airflow. However, autoencoders exhibited better results for both indoor and outdoor studies [138], [139]. Indeed, Masoumi-Verki et al. [137] confirmed that advanced nonlinear methods based on neural networks are promising for the dimensionality reduction step. Upon further study of AEs, it becomes clear that fully connected AEs do not scale well to the problem dimensionality [137]. Convolutional autoencoders (AE-CNN) are better suited for complex fluid dynamics problems, such as those related to urban areas [139], [140], [141]. Masoumi-Verki et al. [141] improved the AE-CNN approach by considering the multi-scale nature of the flow. The authors explained that convolutional layers only capture local correlations among data and may be limited for non-local correlations. To overcome this limitation, they implemented a multi-scale convolutional autoencoder and a self-attention convolutional autoencoder. The study revealed that the self-attention AE-CNN model outperformed the other models in reconstructing the velocity field of a simplified urban geometry. In a similar scenario, Masoumi-Verki et al. [142] demonstrated that adversarial autoencoders performed better than the self-attention AE-CNN in predicting the turbulent kinetic energy of the flow field. Therefore, when POD is inefficient for addressing complex airflows, advanced neural network approaches such as adversarial autoencoder or AE-CNN may successfully reduce dimensionality with reasonable accuracy.

Neural network techniques are also increasingly involved in computing feature dynamics in reduced space. Luo et al. [24] emphasized the limited interpolation ability of RBF and suggested using better interpolators, such as neural networks or SVMs. Recurrent neural networks (e.g., LSTM) or temporal CNN [143] have been successfully used for outdoor urban airflows [137].

Table 2 highlights that advanced machine learning regression techniques such as extreme gradient boosting [144] or LSTMs are already used for built environment applications.

The computational time gains reported for the proposed ROMs are remarkable in the reviewed papers. These models demonstrated reductions in time ranging from 2 to 6 orders of magnitude compared to CFD simulations. However, as with direct surrogate modeling (cf. Section 5.1.3), these results must be balanced with the model’s generalization capabilities and the time required to create the dataset and to train the model. Nevertheless, there is considerable interest in ROM-based control systems that make numerous calls to the model.

While the ROM procedure is powerful, it is essential to recall that ROMs are typically tuned to a specific situation. As Luo et al. [24] stated, the ROM needs to be rebuilt if there are any changes to the geometry or other aspects within the domain. Nevertheless, studies have shown that ROMs can adapt to different boundary conditions [24], [138], [139], [140]. Even if a ROM must be rebuilt, transfer learning techniques appear promising to accelerate this process [24], [142].

Although neural network-based NIROMs have great potential, challenges still need to be addressed. The main weaknesses include the computational cost of training, the physical interpretation of the model, the embedding of physics, and the stability and robustness of the model [137]. Physical interpretation, in particular, is a major challenge for engineering purposes. Classical ROMs (e.g., POD-Galerkin) have the significant advantage of being physically interpretable (see Section 4.3), unlike the black-box models, which have the potential for improving ROM accuracy. Incorporating more physics into these data-driven models is crucial to improve their performance and interpretability. Efforts are already underway to tackle these challenges [137], but they must continue to enable the use of ROMs in increasingly complex and realistic situations.

Although machine learning models can drastically reduce computation, they cannot claim to be as reliable and accurate as CFD simulations. This statement is particularly evident when dealing with long-term simulations, as pure ML predictions can rapidly diverge from physical reality over time (see 5.1.3). Furthermore, as previously discussed, model generalization capabilities are often limited. Simulation reliability is of paramount importance in engineering. It may be acceptable to sacrifice accuracy for computation time for early design, but it is still important to quantify the error, which is challenging. Therefore, relying on an ML model for extrapolation tasks can be risky. To address these limitations, Westermann and Evins [112] discussed gray-box methods, which do not rely solely on data. This approach may offer a better compromise between black-box ML models and classical physics-based simulations. Research is underway to hybridize the two approaches, bridging the gap between pure-ML and pure-CFD methods. As stated in Section 4.1, this may lead to more modest computational gains but with valuable physical consistency.

Several built environment studies explored hybrid approaches.Quang et al. [126] noted that in their future work, it would be essential to investigate whether ML models can accelerate steady-state simulations when used as a warm-up setting for high-accuracy CFD simulations. This strategy could converge faster with excellent accuracy.

Saboori et al. [145] developed an ML-based method to predict the flow behavior and thermal pattern of a large pore-scale porous media Trombe wall incorporating phase change materials. They used high-fidelity CFD results at the micro-scale to train recurrent neural networks. These models enabled them to scale up to large-domain predictions. Thus, they performed long-term simulations and optimized the Trombe wall composition, which is beyond the capabilities of standard numerical methods. We posit that a promising short-term avenue is the data-driven approximation of costly subcomponents, which are subsequently integrated into a classical physics-based simulation.

Mendil et al. [146] introduced a novel hybrid strategy for predicting outdoor pollutant dispersion in 2D sections of urban areas (Fig. 14). This approach combined a simple, fast, and interpretable Gaussian plume model with masking and correction blocks. The masking operation enforced spatial constraints, while the correction stage mitigated inconsistencies using a deep neural network trained on synthetic data. The resulting approach was instantaneous, physically interpretable, and generalizable to any simple urban geometry with reasonable accuracy. Although there are ways to improve the methodology (e.g., 3D predictions, rigorous mass conservation, more complex conditions), this article demonstrated that purely data-driven models are not the only means of enhancing CFD with ML.