Surrogate Model Research Articles

Robust Parameter Design on Dual Stochastic Response Models With Constrained Bayesian Optimization

In engineering system design, minimizing the variations of the quality measurements while guaranteeing their overall quality up to certain levels, namely the robust parameter design (RPD), is crucial. Recent works have dealt with the design of a system whose response-control variables relationship is a deterministic function with a complex shape and function evaluation is expensive. In this work, we propose a Bayesian optimization method for the RPD of stochastic functions. Dual stochastic response models are carefully designed for stochastic functions. The heterogeneous variance of the sample mean is addressed by the predictive mean of the log variance surrogate model in a two-step approach. We establish an acquisition function that favors exploration across the feasible and optimality-improvable regions to effectively and efficiently solve the stochastic constrained optimization problem. The performance of our proposed method is demonstrated by the extensive numerical and case studies. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many manufacturing processes involve undesirable variations, which create variations in the final products. For example, many emerging manufacturing processes, such as nanomanufacturing, involve complex physical and chemical dynamics and transformation, creating variations in the manufacturing output. In such processes, it is crucial to design the manufacturing processes or products so that they have minimum variations in their quality. Meanwhile, it is also important to maintain the overall quality of the designed processes or products. Furthermore, acquiring data from many advanced manufacturing processes is often very costly, especially in the designing stage. In this work, we propose a data-driven method that automatically finds the best setting of manufacturing processes or products with the minimum variations of quality and a given constraint on the average quality satisfied. Our proposed method is used before conducting every experiment; It analyzes the historical data from previous experiments and provides a setting to be used in the next experiment. Our proposed method efficiently utilizes the historical data, and thus finds the best robust setting by conducting only a small number of experiments.

Physics-constrained and flow-field-message-informed graph neural network for solving unsteady compressible flows

With the increasing use of deep neural networks as surrogate models for accelerating computational simulations in mechanics, the application of artificial intelligence in computational fluid dynamics has seen renewed interest in recent years. However, the application of deep neural networks for flow simulations has mainly concentrated on relatively simple cases of incompressible flows. The strongly discontinuous structures that appear in compressible flows dominated by convection, such as shock waves, introduce significant challenges when approximating the nonlinear solutions or governing equations. In this work, we propose a novel physics-constrained, flow-field-message-informed (FFMI) graph neural network for spatiotemporal flow simulations of compressible flows involving strong discontinuities. To enhance the nonlinear approximation capability of strong discontinuities, a shock detector method is leveraged to extract the local flow-field messages. These messages are embedded into the graph representation to resolve the discontinuous solutions accurately. A new FFMI sample-and-aggregate-based message-passing layer, which aggregates the edge-weighted attributes with node features on different hop layers, is then developed to diffuse and process the flow-field messages. Furthermore, an end-to-end paradigm is established within the encoder–decoder framework to transform the extracted information from the flow field into latent knowledge about the underlying fluid mechanics. Finally, a variety of one- and two-dimensional cases involving strong shock waves are considered to demonstrate the effectiveness and generalizability of the proposed FFMI graph neural network.

The reduced-order model of 5 × 5 fuel rod bundles

The fuel rod bundles are the core part of pressurized water reactors (PWRs), and its heat transfer characteristics directly impact the safety of PWRs. A computational fluid dynamics (CFD) model of 5 × 5 fuel rod bundles with a spacer grid is established, and the numerical simulation results are in excellent agreement with the experimental results. Then, the effects of four turbulence models, namely shear stress transport model, standard k–ε model, re-normalization group k–ε model, and realizable k–ε model on the thermal-hydraulic characteristics of the 5 × 5 fuel rod bundles are systematically investigated. Furthermore, two data-driven methods, namely proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are used to analyze the flow fields of the 5 × 5 fuel rod bundles. The two methods can extract key modes or features to enhance the comprehension and description of the dynamic behaviors within the flow fields of 5 × 5 fuel rod bundles. Finally, two reduced-order models (ROMs), called the POD-radial basis function neural network surrogate model and DMD method, are constructed, which can enable rapid prediction of the flow fields for 5 × 5 fuel rod bundles with high accuracy. The CFD simulation results presented in this paper can provide valuable insights for studying the thermal-hydraulic characteristics of the 5 × 5 fuel rod bundles. The two ROMs proposed in this paper can significantly reduce the computational costs associated with studying the thermal-hydraulic characteristics of 5 × 5 fuel rod bundles.

Identification of primary input parameters affecting evacuation in ventilated main control room through CFAST simulations and application of a machine learning algorithm to replace CFAST model

Accurately predicting evacuation time in a ventilated main control room (MCR) during fire emergencies is crucial for ensuring the safety of personnel at nuclear power plants. This study proposes to use neural networks alongside consolidated fire and smoke transport (CFAST) simulations to serve as a surrogate model for physics-based simulation tools. Our neural networks can promptly predict the evacuation time in MCRs, proving to be a valuable asset in fire emergencies and eliminating the need for time-consuming rollouts of the CFAST simulations. The CFAST model simulates fire and evacuation scenarios in a ventilated MCR with variations in input parameters such as door conditions, ventilation flow rate, leakage area, and fire propagation time. Target output parameters, such as hot gas layer temperature (HGLT), heat flux (HF), and optical density (OD), are used alongside standardized evacuation variables to train a machine learning model for predicting evacuation time. The findings suggest that high ventilation flow rates help to dilute smoke and discharge hot gas, leading to lower target output parameters and quicker evacuation. Standardized evacuation variables exceed the required abandonment criteria for all door conditions, indicating the importance of proper evacuation procedures. The results show that neural networks can generate evacuation times close to those obtained from CFAST simulations.

Technology Focus: History Matching and Forecasting (April 2024)

This year’s history matching and forecasting selections cover topics that include a deep-learning framework to forecast spatial/temporal dynamics of CO2 mineralization in reactive rocks, productivity decline analysis using coupled full-field and near-wellbore poromechanics modeling, and a reservoir graph network model for multiwell forecasting in unconventional reservoirs. In paper SPE 216998, the authors present a deep-learning methodology to create surrogate models capable of predicting the precipitation of minerals during CO2 injection into deep saline aquifers. The authors state that this approach allows for the rapid assessment of the individual contributions of each mineral in the CO2 mineralization process. A coupling scheme of a full-field reservoir model and a near-wellbore poromechanics model, its application on productivity index (PI) decline analysis for a deepwater reservoir, and the evaluation of the drawdown effect on well productivity is the subject of paper SPE 212200. According to the authors, the coupling scheme captured geomechanical damages, predicted PI trends with different drawdowns, and enabled identification of safe drawdown limits for operational decisions. The authors of paper URTeC 3855422 present a hybrid approach that combines physics with data-driven approaches for forecasting the performance of unconventional wells under codevelopment. As per the authors, the reservoir graph network model, which describes the drainage volume of an unconventional well using a set of 1D gridblocks parameterized by pore volume and transmissibility, provides an efficient way to model, history-match, and forecast the performance of unconventional wells by reducing the system complexity while maintaining the fundamental physics. Recommended additional reading at OnePetro: www.onepetro.org. URTeC 3862949 A Robust Workflow To Characterize Uncertainties of a Horizontal Well Pad: Multiwell History Matching for Unconventional Reservoirs by Chuxi Liu, The University of Texas at Austin, et al. SPE 212668 Application of Simulation Opportunity Index and Assisted History Matching for Fishbone Completion Strategy in the Existing Single Horizontal Well in a Tight Gas Carbonate Reservoir by Bondan Bernadi, ADNOC, et al. SPE 212723 Automated Production Forecasting Using a Novel Machine-Learning-Based Approach by Kaustubh Shrivastava, SLB, et al.

Multi‐Scale Simulation of a Novel Integrated Reactor for Hydrogen Production by Ammonia Decomposition

AbstractA novel reactor concept for ammonia decomposition utilizing tail gas from a purification unit as heat supply is presented. The designed micro‐structured reactor integrates both endothermic ammonia decomposition and exothermic tail gas combustion. The reactor and corresponding process are simulated using a mathematical multi‐scale model, which combines the results of multiple detailed computational fluid dynamics simulations into a fast surrogate model. The latter is coupled with a process simulation software via a so‐called container to simulate the entire process. The efficiency of the presented reactor concept is determined and benefits over alternative approaches are highlighted.

Enhancing standard CFD based practices for site assessment through polynomial surrogates for estimating uncertainty in wind speed

One of the challenges in digitizing the wind energy sector is to have reliable, accurate and efficient data assessment and prediction tools. We believe that accurate surrogates are key towards improving efficiency and reliability for informed decision making. For a quantitative understanding of wind and energy in complex terrains, a detailed site assessment is done, most often using mesoscale and/or microscale computational fluid dynamics (CFD) based approach. Typically, one would require multiple scenarios/case for a CFD simulator to incorporate the influence of a parameter on variability of wind speed and energy production. These simulations are computationally expensive, and the industry is constantly on a look out for more efficient methods. Towards this end, we propose using a polynomial surrogate based on Polynomial Chaos Expansion (PCE) for uncertainty quantification that requires only a few CFD simulations to assess the variability of wind speed with respect to variability in an input parameter. The variability estimates from PCE were first validated against the standard Monte Carlo method on simple benchmarks and then tested for complex terrains. In this work, we present results that help us understand how canopy foliage, particularly its height, impacts the variability in wind speed in complex terrains. Since the polynomial surrogate relies only on a limited set of input variations (forest height) to estimate the variability distributions for wind speed locally (for specified points of interests), it has proven to be a low-cost and accurate method for estimating uncertainty. In this paper, we discuss the results for wind speed variability for five sites with varying complexity using the polynomial surrogate model. Furthermore, the singular value decomposition (SVD) entropy value is used to quantify terrain complexity for the sites considered. We show how the variability in wind speed can potentially be correlated to terrain complexity. This is our first attempt in providing an empirically (including multiple sites) derived relationship that can be used as a basis for fast and reliable variability estimator for wind resource planners.

Sensitivity of cholinesterases and carboxylesterases to pharmaceutical products in Tinca tinca.

Discharges to the aquatic environment of pharmaceuticals represent a hazard to the aquatic organisms. Subchronic assay with 17-alpha-ethinylestradiol (EE2) and in vitro essays with pharmaceuticals of environmental concern were conducted to examine the sensitivity of tissue acetylcholinesterase (AChE) and carboxylesterase (CbE) activities of Tinca tinca to them. Subchronic exposure to 17-alpha-EE2 caused significant effects on brain, liver, and muscle CbE, but no on AChE activities. Most of the pharmaceuticals tested in vitro were considered as weak inhibitors of tissular AChE activity. Depending on the tissues, some compounds were classified as moderate inhibitors of CbE activity while other were categorized as weak enzymatic inhibitors. An opposite trend was observed depending on the tissue, while brain and liver CbE activities were inhibited, the muscle CbE activity was induced. Changes experienced on enzymatic activities after exposure to pharmaceuticals might affect the physiological functions in which these enzymes are involved. In vitro exposure to 17-alpha-EE2 in tench could be an informative, but not a surrogate model to know the effect of this synthetic estrogen on AChE and CbE activities.

Study and optimization of a deformable trimaran amphibious transport vehicle's resistance characteristic

Amphibious transport vehicles have increasingly become an important tool for connecting water and land transportation, serving both water and land transport missions. However, due to the unique shape of amphibious vehicles, their sailing resistance is high, which severely restricts their widespread use. In this paper, a deformable trimaran amphibious transport vehicle with retractable side hulls is designed. Based on the Reynolds-averaged Navier–Stokes equation, a resistance prediction method for amphibious vehicles is established and verified through towing experiments. The resistance characteristic of the trimaran vehicle is studied and optimized. First, the effects of the side hull and its position on resistance performance are analyzed, and the sensitivity of position parameters is evaluated. Then, the bow plate angle on resistance is analyzed. Finally, a surrogate model of the side hull position parameters and the bow plate angle with resistance is established using the Kriging method. The Particle Swarm Optimization is used to search for the minimum resistance configuration Opt 2, which achieves a drag reduction effect of 19.84% at the design speed.

A comprehensive deep learning geometric shape optimization framework with field prediction surrogate and reinforcement learning

The optimization of aerodynamic components' geometric shapes demands a novel technical approach for adaptive and efficient exploration and decision-making within the design space. In this study, we introduce an innovative shape optimization framework that leverages deep reinforcement learning with neural network surrogate models. The field prediction surrogate, realized by two distinct U-net architectures, can efficiently generate holistic field solutions based on the transformed mesh coordinates. Subsequently, an inference engine dynamically calculates the key metric of the flow fields, serving as the objective function for the subsequent geometry-aware Deep Q network (DQN)-based optimization. The framework's efficacy is validated using a rocket nozzle as an illustrative example. During surrogate validation, under both friction and frictionless conditions, the l1 errors of the entire flow field of both the U-net vision transformer (ViT) and U-net convolutional neural network (CNN) architectures are less than 0.4%. The proposed U-net ViT consistently outperforms U-net CNN, and the superiority is particularly evident in complex flow areas, outlet sections, and vacuum thrust prediction. Following training, the DQN model is employed to explore the design variable space. The B-spline defining profile successfully is optimized to a final expanding segment shape with improved thrust. Under frictionless conditions, it closely approaches the theoretical optimum. In the practical condition considering friction, the optimized shape gains a 2.96% thrust improvement. The results demonstrate that the proposed framework, especially when coupled with U-net ViT, exhibits enhanced accuracy and adaptability for shape optimization tasks.

An accurate and efficient deep learning model for spatio-temporal prediction of interfacial flows

Aiming at fast and accurate spatiotemporal prediction of interfacial flow fields, a novel deep learning model combining Convolutional AutoEncoder (CAE) and long short-term memory with spatial and temporal attention (LSTM-STA) is proposed and named as CAE-LSTM-STA (hybrid model of CAE and LSTM-STA) in this article. To enable a fast calculation process, CAE is first utilized to compress the high-dimensional snapshots of flow fields into the low-dimensional latent space by its encoder. Then, the latent space serves as the input feature for LSTM-STA to temporally evolve the state of the low-dimensional latent space. Finally, the low-dimensional latent space at future time steps is fed back into the decoder of CAE to derive the full-order snapshots of the flow fields. The prediction performance of the proposed model is evaluated via two representative benchmark cases, including the dam break case and the rising bubble case. The capability of CAE in dimension reduction is found to be much better than that of the widely used Proper Orthogonal Decomposition, while LSTM-STA is observed that outperforms the original LSTM in multivariant temporal prediction. These promising results indicate that the proposed CAE-LSTM-STA model is able to effectively capture and advance the spatiotemporal characteristics of the interfacial flow fields, therefore making it an advanced surrogate model for fast and precise generation of the temporally continuous interfacial flow fields.

Composing MPC With LQR and Neural Network for Amortized Efficiency and Stable Control

Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common solutions include explicit MPC and function approximation. Both methods, whenever applicable, may improve the computational efficiency of the implicit MPC by several orders of magnitude. Nevertheless, explicit MPC often requires expensive pre-computation and does not easily apply to higher-dimensional problems. Meanwhile, function approximation, although scales better with dimension, still requires pre-training on a large dataset and generally cannot guarantee to find an accurate surrogate policy, the failure of which often leads to closed-loop instability. To address these issues, we propose a triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining a linear quadratic regulator, a neural network, and an MPC. From its standard form, we derive two variants of such hybrid control scheme: one customized for chaotic systems and the other for slow systems. The proposed scheme does not require pre-computation and is capable of improving the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amortized</i> running time of the composed MPC with a well-trained neural network. In addition, the scheme maintains closed-loop stability with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">any</i> neural networks of proper input and output dimensions, alleviating the need for certifying optimality of the neural network in safety-critical applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the need to reduce the amortized cost of MPC in repetitive industrial robotic applications, where long-term operational cost is important and safety is critical. Examples of such applications include factory robotic arm manipulation and fixed-route quadcopter payload transport. Unlike explicit MPC or function approximation, our approach does not require any pre-computation or pre-training. Rather, it attains task proficiency over time by learning a surrogate neural network on the spot and by gradually replacing the costly MPC with the more efficient surrogate model so long as safety permits. Consequently, the proposed scheme incurs a learning cost during the initial phase of the deployment but usually becomes more adept on the task afterwards, leading to amortized efficiency.

A Data-Driven Surrogate Modeling for Train Rescheduling in High-Speed Railway Networks Under Wind-Caused Speed Restrictions

A Data-Driven Surrogate Modeling for Train Rescheduling in High-Speed Railway Networks Under Wind-Caused Speed Restrictions

Large-scale optimization of nonconvex MINLP refinery scheduling

Modeling and optimization of large-scale refinery scheduling problems is challenging because of their complexity and size. Herein, we propose a mathematical model to represent such problems more accurately and realistically, and a state-of-the-art optimization framework for its solution. The framework leverages the use of mathematical optimization and algorithmic methods by combining modeling approaches (process design, model decompositions), solving strategies (rescheduling, heuristics), and machine learning regression (surrogate models). An industrial-size refinery scheduling problem (2 blenders, 4 feed tanks, distillation network with 5 towers, processing network with FCC, hydrotreaters, debutanizers, superfractionator, catalytic reformer) is formulated as a hierarchical nonconvex mixed-integer nonlinear programming (MINLP) model and is successfully optimized, providing higher profitability and more efficient scheduling operations considering 12 feedstocks, 10 products and multiple scenarios for time horizon and step. Results highlight the importance of tuning scheduling parameters and employing an enhanced computer-aided framework to enable the solution of industrial refinery scheduling operations.

Analysis of the LatticeNet neural network framework’s performance using prediction-calculated temperature coefficients in PWR assemblies

Various Machine Learning (ML) techniques have seen recent and growing interest in the creation of surrogate neutronics models as a potential way to avoid the computational expenses associated with conventional high-fidelity modeling. Artificial Neural Networks (ANNs) have been shown to be particularly useful for single-assembly predictions involving pin-wise power distributions and multiplication factors. In this paper, the LatticeNet neural network framework is investigated as a method to predict Doppler and moderator temperature coefficients for Pressurized Water Reactor (PWR) fuel assemblies, as well as differential boron worth. This approach uses the built-in tools developed alongside LatticeNet to construct two fully-connected network architectures capable of predicting k-eigenvalues from two inputs such as fuel enrichment and temperature when trained with data generated with CASMO-4E. A single network taking in all study parameters as inputs was then used to predict k-eigenvalues for fuel temperature, moderator temperature, and boron perturbation cases. The calculated temperature coefficients and differential boron worth values were compared with a bank of reference values to validate the efficacy of this method. Overall, differences in k-eigenvalues were within 0.017% in the worst case. The temperature coefficients saw mean errors of 1.85% and 1.69% for the two-parameter networks, respectively. The all-parameter network was then shown to predict 1100 points in 236 ms compared to the 4.95 min CASMO-4E took to generate them. Additionally, the differential boron worth achieved the lowest mean error of 0.30%; each of these values were within our acceptance criteria.

Accelerated Bayesian Inference for Molecular Simulations using Local Gaussian Process Surrogate Models.

While Bayesian inference is the gold standard for uncertainty quantification and propagation, its use within physical chemistry encounters formidable computational barriers. These bottlenecks are magnified for modeling data with many independent variables, such as X-ray/neutron scattering patterns and electromagnetic spectra. To address this challenge, we employ local Gaussian process (LGP) surrogate models to accelerate Bayesian optimization over these complex thermophysical properties. The time-complexity of the LGPs scales linearly in the number of independent variables, in stark contrast to the computationally expensive cubic scaling of conventional Gaussian processes. To illustrate the method, we trained a LGP surrogate model on the radial distribution function of liquid neon and observed a 1,760,000-fold speed-up compared to molecular dynamics simulation, beating a conventional GP by three orders-of-magnitude. We conclude that LGPs are robust and efficient surrogate models poised to expand the application of Bayesian inference in molecular simulations to a broad spectrum of experimental data.

Data-driven models of nonautonomous systems

Nonautonomous dynamical systems are characterized by time-dependent inputs, which complicates the discovery of predictive models describing the spatiotemporal evolution of the state variables of quantities of interest from their temporal snapshots. When dynamic mode decomposition (DMD) is used to infer a linear model, this difficulty manifests itself in the need to approximate the time-dependent Koopman operators. Our approach is to approximate the original nonautonomous system with a modified system derived via a local parameterization of the time-dependent inputs. The modified system comprises a sequence of local parametric systems, which are subsequently approximated by a parametric surrogate model using the DRIPS (dimension reduction and interpolation in parameter space) framework. The offline step of DRIPS relies on DMD to build a linear surrogate model, endowed with reduced-order bases for the observables mapped from training data. The online step interpolates on suitable manifolds to construct a sequence of iterative parametric surrogate models; the target/test parameter points on these manifolds are specified by a local parameterization of the test time-dependent inputs. We use numerical experimentation to demonstrate the robustness of our method and compare its performance with that of deep neural networks.

Design and validation of refractory alloys using machine learning, CALPHAD, and experiments

Refractory multicomponent alloys (RMCAs) have garnered attention as potential materials for high-temperature structural applications, due to their excellent mechanical properties. However, conventional alloy design has limitations in terms of constrained compositional space and a lack of computational databases with adequate coverage. To address this, we present a design framework that leverages machine learning (ML), the CALculation of PHAse Diagram (CALPHAD) method, and experimental validation to efficiently develop refractory alloys. The present study focuses on the Mo-Nb-W ternary system. Six ternary alloys were inversely designed by means of the conditional generative adversarial network (cGAN) and fabricated via arc melting. The ternary alloys exhibit a single BCC phase which is consistent with CALPHAD calculations as well as Scheil simulations. The present interactive design loop between the ML surrogate model and experiments is demonstrated through the accurate hardness prediction, resulting in cGAN models capable of rapid exploration of the higher-order design space. The hardness of the Mo-Nb-W alloys is in the range of 5–6 GPa due to their solid solution strengthening.

Parameterized Reduced-Order Models for Probabilistic Analysis of Thermal Protection System Based on Proper Orthogonal Decomposition

The thermal protection system (TPS) represents one of the most critical subsystems for vehicle re-entry. However, due to uncertainties in thermal loads, material properties, and manufacturing deviations, the thermal response of the TPS exhibits significant randomness, posing considerable challenges in engineering design and reliability assessment. Given that uncertain aerodynamic heating loads manifest as a stochastic field over time, conventional surrogate models, typically accepting scalar random variables as inputs, face limitations in modeling them. Consequently, this paper introduces an effective characterization approach utilizing proper orthogonal decomposition (POD) to represent the uncertainties of aerodynamic heating. The augmented snapshots matrix is used to reduce the dimension of the random field by the decoupling method of independently spatial and temporal bases. The random variables describing material properties and geometric thickness are also employed as inputs for probabilistic analyses. An uncoupled POD Gaussian process regression (UPOD-GPR) model is then established to achieve highly accurate solutions for transient heat conduction. The model takes random heat flux fields as inputs and thermal response fields as outputs. Using a typical multi-layer TPS and thermal structure as two examples, probabilistic analyses are conducted. The mean square relative error of a typical multi-layer TPS is less than 4%. For the thermal structure, the averaged absolute error of the radiation and insulation layer is less than 25 °C and 6 °C when the maximum reaches 1200 °C and 150 °C, respectively. This approach can provide accurate and rapid predictions of thermal responses for TPS and thermal structures throughout their entire operating time when furnished with input heat flux fields and structural parameters.

Data-Driven Car Drag Prediction With Depth and Normal Renderings

Abstract Generative artificial intelligence (AI) models have made significant progress in automating the creation of 3D shapes, which has the potential to transform car design. In engineering design and optimization, evaluating engineering metrics is crucial. To make generative models performance-aware and enable them to create high-performing designs, surrogate modeling of these metrics is necessary. However, the currently used representations of 3D shapes either require extensive computational resources to learn or suffer from significant information loss, which impairs their effectiveness in surrogate modeling. To address this issue, we propose a new 2D representation of 3D shapes. We develop a surrogate drag model based on this representation to verify its effectiveness in predicting 3D car drag. We construct a diverse dataset of 4535 high-quality 3D car meshes labeled by drag coefficients computed from computational fluid dynamics simulations to train our model. Our experiments demonstrate that our model can accurately and efficiently evaluate drag coefficients with an R2 value above 0.84 for various car categories. Our model is implemented using deep neural networks, making it compatible with recent AI image generation tools (such as stable diffusion) and a significant step toward the automatic generation of drag-optimized car designs. Moreover, we demonstrate a case study using the proposed surrogate model to guide a diffusion-based deep generative model for drag-optimized car body synthesis.