Surrogate Model Research Articles

Characterization of bi-segmented and tri-segmented recombinant Pichinde virus particles.

Mammarenaviruses include several highly virulent pathogens (e.g., Lassa virus) capable of causing severe hemorrhagic fever diseases for which there are no approved vaccines and limited treatment options. Mammarenaviruses are enveloped, bi-segmented ambisense RNA viruses. There is limited knowledge about cellular proteins incorporated into progeny virion particles and their potential biological roles in viral infection. Pichinde virus (PICV) is a prototypic arenavirus used to characterize mammarenavirus replication and pathogenesis. We have developed a recombinant PICV with a tri-segmented RNA genome as a viral vector platform. Whether the tri-segmented virion differs from the wild-type bi-segmented one in viral particle morphology and protein composition has not been addressed. In this study, recombinant PICV (rPICV) virions with a bi-segmented (rP18bi) and a tri-segmented (rP18tri) genome were purified by density-gradient ultracentrifugation and analyzed by cryo-electron microscopy and mass spectrometry. Both virion types are pleomorphic with spherical morphology and have no significant difference in size despite rP18tri having denser particles. Both virion types also contain similar sets of cellular proteins. Among the highly enriched virion-associated cellular proteins are components of the endosomal sorting complex required for transport pathway and vesicle trafficking, such as ALIX, Tsg101, VPS, CHMP, and Ras-associated binding proteins, which have known functions in virus assembly and budding. Other enriched cellular proteins include peripheral and transmembrane proteins, chaperone proteins, and ribosomal proteins; their biological roles in viral infection warrant further analysis. Our study provides important insights into mammarenavirus particle formation and aids in the future development of viral vectors and antiviral discovery.IMPORTANCEMammarenaviruses, such as Lassa virus, are enveloped RNA viruses that can cause severe hemorrhagic fever diseases (Lassa fever) with no approved vaccine and limited therapeutic options. Cellular proteins incorporated into progeny virion particles and their biological roles in mammarenavirus infection have not been well characterized. Pichinde virus (PICV) is a prototypic mammarenavirus used as a surrogate model for Lassa fever. We used cryo-electron microscopy and proteomic analysis to characterize the morphology and protein contents of the purified PICV particles that package either two (bi-segmented) or three (tri-segmented) genomic RNA segments. Our results demonstrate a similar virion morphology but different particle density for the bi- and tri-segmented viral particles and reveal major virion-associated cellular proteins. This study provides important insights into the virus-host interactions that can be used for antiviral development and optimizing arenavirus-based vaccine vectors.

Optimizing Flow and Heat Transfer With Guiding Pin Fins in a Wedge-Shaped Cooling Channel for Gas Turbine Blade Trailing Edge

Abstract In this study, an innovative guiding pin-fin array optimization has been developed through three-dimensional numerical simulations to enhance the cooling efficiency of gas turbine blade trailing edge. The guiding pin-fin array is optimized using the Kriging surrogate model and Genetic Algorithm (GA), aiming to significantly improve the heat transfer rates and uniformity within the wedge-shaped channel. The design parameter chosen for optimization is the deflection angle of each guiding pin fin, and the optimization process is conducted in two rounds. The first-round optimization yields a first-optimized guiding pin-fin array, which exhibits superior overall heat transfer performance and reasonable pressure loss compared to conventional circular, oblong, and parallel pin-fin arrays. For the first-optimized guiding pin-fin (1st-OGP) channel at the Reynolds number of Re = 50,000, the total Nusselt number and pressure loss are 44.1% higher and 9.9% lower than those of the baseline circular pin-fin array (CP), respectively. An experimental validation using the transient liquid crystal (TLC) thermography method is carried out and proves the effectiveness of the optimization process. However, it is noted that the first-optimized guiding pin-fin exhibits even lower heat transfer at a low Reynolds number of Re = 10,000, particularly in the channel middle region, which is mainly due to the incapable turning flow control in the root region of the wedged channel. To address this issue and further improve the heat transfer performance at low Reynolds numbers, a second-round optimization is performed by specifically adjusting the deflection angle of the selected guiding pin fins near the root region of the wedged channel. This secondary optimization demonstrates significant heat transfer improvements over the whole studied Reynolds number range with a reasonably reduced consumption of computational resources. The total Nusselt number and pressure loss are 69.3% higher and 11.9% lower than those of the baseline circular pin-fin array, respectively, at Re = 50,000. The optimization process proposed in this paper produces a high-performance cooling structure design with elaborate guiding pin-fin arrangements in the wedge-shaped channel, which indicates high heat transfer enhancement and relatively lower pressure loss in the wedged channel for the turbine blade trailing edge.

A novel machine learning framework for impact force prediction of foam-filled multi-layer lattice composite structures

Numerical simulations can provide valuable insights for the optimization of design and operational management; however, they are often impractical and computationally intensive. Machine learning methods are appealing to these problems due to their sufficient efficiency and accuracy. In this study, a novel framework for predicting the impact responses of foam-filled multi-layer lattice composite structures (FMLCSs) was proposed by combining the accurate finite element (FE) analyses, surrogate models, fast Fourier transform (FFT) method, and inverse FFT (IFFT) method. Firstly, reliable FM models were established to simulate the crashworthiness of the five FMLCSs under impact loading, including an analysis of energy transformation. Subsequently, surrogate models, namely radial basis function (RBF), polynomial response surface (PRS), Kriging (KRG), and back propagation neural network (BPNN), combined with methods of FFT and IFFT, were employed to predict the impact force-time series of the FMLCSs. More than 1000 frequency points were employed for each type of FMLCS, and all the R-square (R2) values of the established surrogate models exceeded 0.95, indicating that the proposed framework accurately predicted the impact duration and impact responses in the frequency domain. In addition, parameter sensitivity analysis revealed that a high peak impact force was accompanied by a short impact duration. Moreover, increasing the lattice-web height resulted in a significant increase in the impact duration.

Topology-Agnostic Graph U-Nets for Scalar Field Prediction on Unstructured Meshes

Abstract Machine-learned surrogate models to accelerate lengthy computer simulations are becoming increasingly important as engineers look to streamline the product design cycle. In many cases, these approaches offer the ability to predict relevant quantities throughout a geometry, but place constraints on the form of the input data. In a world of diverse data types, a preferred approach would not restrict the input to a particular structure. In this paper, we propose Topology-Agnostic Graph U-Net (TAG U-Net), a graph convolutional network that can be trained to input any mesh or graph structure and output a prediction of a target scalar field at each node. The model constructs coarsened versions of each input graph and performs a set of convolution and pooling operations to predict the node-wise outputs on the original graph. By training on a diverse set of shapes, the model can make strong predictions, even for shapes unlike those seen during training. A 3-D additive manufacturing dataset is presented, containing Laser Powder Bed Fusion simulation results for thousands of parts. The model is demonstrated on this dataset, and it performs well, predicting both 2-D and 3-D scalar fields with a median R-squared > 0.85 on test geometries.

Data-driven predictions of retained austenite content and yield strength and elucidation of the sliding wear performance of carbide-free bainitic steels

Carbide-free bainitic (CFB) steels have drawn much attention due to their high strength and toughness. The present work aims to build machine learning (ML) based surrogate models to predict retained austenite (RA) content and yield strength (YS) of isothermal transformed CFB steels and study the sliding wear performance. The input data for ML prediction were related to compositions, heat treatment process, and phases. The Random Forest regression and Gaussian process regression were respectively selected to build the predictive models for RA content and YS. Result shows that the predicted RA content agrees well with the experimentally determined ones in steel with high stability of untransformed austenite. For YS prediction, the present surrogate model can predict YS of CFB steels even without additional microstructural information such as dislocation and effective substructure size. Steels with different YS and RA content were designed to study the sliding wear performance. Result shows that the dominant wear mechanism of the tested steels is abrasive wear and the weight loss is inversely proportional to hardness when the load and wear distance are constant. Increasing YS and RA content can increase the initial hardness and work hardening ability at the worn surface, thereby enhancing wear resistance.

High-efficient sample point transform algorithm for large-scale complex optimization

Decomposition algorithms and surrogate model methods are frequently employed to address large-scale, intricate optimization challenges. However, the iterative resolution phase inherent to decomposition algorithms can potentially alter the background vector, leading to the repetitive evaluation of samples across disparate iteration cycles. This phenomenon significantly diminishes the computational efficiency of optimization. Accordingly, a novel approach, designated the Sample Point Transformation Algorithm (SPTA), is put forth in this paper as a means of enhancing efficiency through a process of mathematical deduction. The mathematical deduction reveals that the difference between sample points in each iteration loop is a simple function related to the inter-group dependent variables. Consequently, the SPTA method achieves the comprehensive transformation of the sample set by establishing a surrogate model of the difference between the sample sets of two cycles with a limited number of sample points, as opposed to conducting a substantial number of repeated samplings. This SPTA is employed to substitute the most time-consuming step of direct calculation in the classical optimization process. To validate the calculation efficiency, a series of numerical examples were conducted, demonstrating an improvement of approximately 75 % while maintaining optimal accuracy. This illustrates the advantage of the SPTA in addressing large-scale and complex optimization problems.

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution.Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(nlogn) instead of the typical O(n3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

Driving Control Strategy and Specification Optimization for All-Wheel-Drive Electric Vehicle System with a Two-Speed Transmission

Equipping electric vehicles with a two-speed gearbox allows for achieving high torque and maximum speed through appropriate gear ratio adjustments. Additionally, tuning motor operating points to efficient zones, considering energy efficiency, significantly enhances the vehicle’s overall performance. This paper presents an AWD system configuration method, integrating a two-speed transmission to improve energy efficiency and driving performance through front and rear motor torque distribution and powertrain specification optimization. Based on vehicle simulations conducted using MATLAB/Simulink, a strategy for torque distribution between the front/rear axles was established using fuzzy logic, considering energy efficiency and driving stability. Furthermore, a multi-objective optimization was performed using a surrogate model trained through MATLAB parallel simulations. When the optimization results were applied to various vehicle specifications, it was observed that energy efficiency was improved, and acceleration performance was increased compared to a baseline vehicle without optimization.

ViscoNet: A lightweight FEA surrogate model for polymer nanocomposites viscoelastic response prediction

Polymer-based nanocomposites (PNCs) are formed by dispersing nanoparticles (NPs) within a polymer matrix, which creates polymer interphase regions that drive property enhancement. However, data-driven PNC design is challenging due to limited data. To address the challenge, we present ViscoNet, a surrogate model for finite element analysis (FEA) simulations of PNC viscoelastic (VE) response. ViscoNet leverages pre-training and finetuning to accelerate predicting VE response of a new PNC system. By predicting the entire VE response, ViscoNet surpasses previous scalar-based surrogate models for FEA simulation, offering better fidelity and efficiency. We explore ViscoNet's effectiveness through generalization tasks, both within thermoplastics and from thermoplastics to thermosets, reporting a mean absolute percentage error (MAPE) of < 5 % for rubbery modulus and < 1 % for glassy modulus in all cases and 1.22 % on tan δ peak height prediction. With only 500 FEA simulations for finetuning, ViscoNet can generate over 20k VE responses within 2 min with 1 CPU, compared to 97 days with 4 CPUs via FEA simulations.

Boosting Engineering Optimization With a Novel Recursive Transfer Bifidelity Surrogate Modeling

Abstract In the engineering optimization, there often exist the multiple sources of information with different fidelity levels. In general, low-fidelity (LF) information is usually more accessible than high-fidelity (HF) information, while the latter is usually more accurate than the former. Thus, to capitalize on the advantages of this information, this study proposes a novel recursive transfer bifidelity surrogate modeling to fuse information from HF and LF levels. First, the selection method of optimal scale factor is proposed for constructing bifidelity surrogate model. Then, a recursive method is developed to further improve its performance. The efficacy of the proposed model is comprehensively evaluated using numerical problems and an engineering example. Comparative analysis with some surrogate models (five multifidelity and a single-fidelity surrogate models) demonstrates the superior prediction accuracy and robustness of the proposed model. Additionally, the impact of varying cost ratios and combinations of HF and LF samples on the performance of the proposed model is also investigated, yielding consistent results. Overall, the proposed model has superior performance and holds potential for practical applications in engineering design optimization problems.

Data-Efficient Dimensionality Reduction and Surrogate Modeling of High-Dimensional Stress Fields

Abstract Tensor datatypes representing field variables like stress, displacement, velocity, etc., have increasingly become a common occurrence in data-driven modeling and analysis of simulations. Numerous methods [such as convolutional neural networks (CNNs)] exist to address the meta-modeling of field data from simulations. As the complexity of the simulation increases, so does the cost of acquisition, leading to limited data scenarios. Modeling of tensor datatypes under limited data scenarios remains a hindrance for engineering applications. In this article, we introduce a direct image-to-image modeling framework of convolutional autoencoders enhanced by information bottleneck loss function to tackle the tensor data types with limited data. The information bottleneck method penalizes the nuisance information in the latent space while maximizing relevant information making it robust for limited data scenarios. The entire neural network framework is further combined with robust hyperparameter optimization. We perform numerical studies to compare the predictive performance of the proposed method with a dimensionality reduction-based surrogate modeling framework on a representative linear elastic ellipsoidal void problem with uniaxial loading. The data structure focuses on the low-data regime (fewer than 100 data points) and includes the parameterized geometry of the ellipsoidal void as the input and the predicted stress field as the output. The results of the numerical studies show that the information bottleneck approach yields improved overall accuracy and more precise prediction of the extremes of the stress field. Additionally, an in-depth analysis is carried out to elucidate the information compression behavior of the proposed framework.

Analysis and optimization of the dynamic response characteristics of aircraft cargo rack

In order to effectively achieve the optimization design of the aircraft cargo rack, based on finite element modal simulation, the structure was redesigned and analyzed using two schemes of surrogate model size optimization and topology optimization, ensuring the strength requirements while improving the natural frequency and reducing the weight. According to the modal shape of vibration, additional bridge structures were added at the weak points to improve the dynamic stiffness of the structure. According to the optimization design requirements, the response surface function was constructed, and the particle swarm optimization algorithm was applied in the size optimization and surrogate model solution. A multi-objective optimization model was established for flexibility and low-order natural frequencies, and topology optimization was carried out in HyperWorks. The structural dynamic modification of the topology optimization model was performed using the modal strain energy analysis method. The research results show that both optimization methods can achieve good lightweight design. The static performance of the optimized structure is stable, and the overall modal frequency is improved.

Preventive Preservation of Rammed Earth Historical Heritage Through Continuous Monitoring, Architectural Inspections, and Data Fusion

Rammed earth construction, an ancient and sustainable building technique, faces significant preservation challenges, particularly in historical contexts. This study aims to enhance the preventive preservation of rammed earth historical heritage through a comprehensive methodology combining continuous monitoring, architectural inspections, and data fusion. By integrating nondestructive testing techniques such as ultrasound, thermography, and ground-penetrating radar with operational modal analysis and modeling, the proposed approach allows for early detection and assessment of structural vulnerabilities. This methodology was applied to the Tower of Muhammad in the Alhambra of Granada, Spain, demonstrating its effectiveness in identifying and quantifying damage and predicting structural health. Using multi-source data (documentation, inspections, nondestructive tests, and continuous monitoring), a finite element model was built, calibrated (achieving an avg. error in modal frequencies of 1.28% and a minimum modal assurance criterion value of 0.94), and used to develop a surrogate model able to predict the modal properties of the tower in 0.02 s, becoming compatible with continuous system identification. The presented results highlight the importance of continuous data acquisition and advanced diagnostic tools for safeguarding rammed earth structures against environmental and anthropogenic threats. This study advocates for the adoption of digital twins in historical preservation, facilitating informed decision-making and sustainable management of cultural heritage.

Bayesian protocols for high-throughput identification of kinematic hardening model forms

Constitutive models are essential for assessing the mechanical response of complex materials, yet uncertainties in model forms and parameters persist due to the influence of micromechanisms and microstructural features. We develop Bayesian protocols to iteratively refine both model forms and the associated material properties for complex constitutive models. Our aim is to provide rigorous, probabilistically informed evaluations of improvements achieved with increasing model complexity. Leveraging high-throughput experimental microindentation data, the protocols involve three steps: (i) emulating FE simulations using multi-output Gaussian process surrogate models, (ii) calibrating an initial simple constitutive model against experimental data, and (iii) progressively enhancing model complexity by iteratively improving agreement between simulations and experiments. The various model forms are compared using model form probabilities and aggregate discrepancies. Sobol indices are used to quantify the identifiability of material properties, aiming to prevent parameter proliferation. We apply this protocol to identify the optimal form of cyclic plasticity models for duplex Ti-6Al-4V. Although tailored for cyclic plasticity models, these protocols hold promise for calibrating and refining nonlinear constitutive models across diverse material classes.

SORM‐Enhanced Inverse Reliability Analysis for Geotechnical Multiobjective Reliability‐Based Design Optimization

ABSTRACTThe first‐order reliability method (FORM) is mostly employed in the existing geotechnical reliability‐based design (RBD) methods due to its computational simplicity and efficiency. However, the first‐order Taylor approximation of the limit state surface (LSS) may result in significant errors, especially in cases of highly nonlinear LSS characterized by substantial curvatures. Therefore, FORM‐based RBD methods require a modification of the curvatures to enhance the accuracy of the probabilistic constraints, specifically by converting the target reliability index into a more precise target failure probability. Correspondingly, reliability index‐based design is converted into failure probability‐based design. In this study, the parabolic second‐order reliability method (SORM), which avoids the Hessian calculations, is adopted to improve the accuracy of probabilistic constraints beyond what is achievable with FORM. The proposed SORM‐enhanced RBD method accounts for the curvature information of the nonlinear LSS, modifying the target reliability index to align with the exact target failure probability through the application of SORM. Moreover, by incorporating an implicit coupling function, multiobjective RBD can be effectively implemented without any additional surrogate model. Furthermore, the proposed RBD method is readily extended to reliability‐based design optimization (RBDO) through integration with an optimization strategy. The proposed RBDO method demonstrates a more precise convergence of the probabilistic constraints, surpassing the accuracy of FORM‐based RBDO methods. Notably, the proposed SORM‐enhanced RBDO method not only significantly improves accuracy but also bypasses the necessity for Hessian computation, which remains both the second‐order accuracy and first‐order efficiency. The feasibility of the proposed method is demonstrated through a mathematical example and three practical geotechnical design examples.

Trainability maximization using estimation of distribution algorithms assisted by surrogate modelling for quantum architecture search

Quantum architecture search (QAS) involves optimizing both the quantum parametric circuit configuration but also its parameters for a variational quantum algorithm. Thus, the problem is known to be multi-level as the performance of a given architecture is unknown until its parameters are tuned using classical routines. Moreover, the task becomes even more complicated since well-known trainability issues, e.g., barren plateaus (BPs), can occur. In this paper, we aim to achieve two improvements in QAS: (1) to reduce the number of measurements by an online surrogate model of the evaluation process that aggressively discards architectures of poor performance; (2) to avoid training the circuits when BPs are present. To detect the presence of the BPs, we employed a recently developed metric, information content, which only requires measuring the energy values of a small set of parameters to estimate the magnitude of cost function’s gradient. The main idea of this proposal is to leverage a recently developed metric which can be used to detect the onset of vanishing gradients to ensure the overall search avoids such unfavorable regions. We experimentally validate our proposal for the variational quantum eigensolver and showcase that our algorithm is able to find solutions that have been previously proposed in the literature for the Hamiltonians; but also to outperform the state of the art when initializing the method from the set of architectures proposed in the literature. The results suggest that the proposed methodology could be used in environments where it is desired to improve the trainability of known architectures while maintaining good performance.

Predicting the variability of the dynamics of bolted joints using polynomial chaos expansion

Friction and contact occurring in bolted joints can lead to highly nonlinear dynamics. Moreover, joints are prone to high sample-to-sample variability as well as low test-to-test repeatability. Notably, experimental work is increasingly highlighting the most influential sources of uncertainties. Nevertheless, randomness due to some uncertainties, such as surface imperfections, cannot be completely eliminated. Others, such as the actual applied bolt load, can be laborious to control. In this work, we aim to computationally predict the variability of numerical models of joints given such uncertainties. We perform the dynamic analysis using the Multi-Harmonic Balance Method (MHBM) to compute the forced, periodic response of the system. For probabilistic surrogate modeling, we use Polynomial Chaos Expansion (PCE). We show that PCE can be successful in studying the impact of ISO tolerances and uncertain bolt loads in the practical case where only a few numerical samples can be generated. We also show that an empirical error metric is unreliable and a validation error metric must be used. In addition, we assess using PCE to propagate uncertainties due to mesoscale imperfections, and highlight that unsuccessful PCE models indicate sensitive structural designs.

Efficient Ensemble Adversarial Attack for a Deep Neural Network (DNN)-Based Unmanned Aerial Vehicle (UAV) Vision System

In recent years, unmanned aerial vehicles (UAVs) vision systems based on deep neural networks (DNNs) have made remarkable advancements, demonstrating impressive performance. However, due to the inherent characteristics of DNNs, these systems have become increasingly vulnerable to adversarial attacks. Traditional black-box attack methods typically require a large number of queries to generate adversarial samples successfully. In this paper, we propose a novel adversarial attack technique designed to achieve efficient black-box attacks with a minimal number of queries. We define a perturbation generator that first decomposes the image into four frequency bands using wavelet decomposition and then searches for adversarial perturbations across these bands by minimizing a weighted loss function on a set of fixed surrogate models. For the target victim model, the perturbation images generated by the perturbation generator are used to query and update the weights in the loss function, as well as the weights for different frequency bands. Experimental results show that, compared to state-of-the-art methods on various image classifiers trained on ImageNet (such as VGG-19, DenseNet-121, and ResNext-50), our method achieves a success rate over 98% for targeted attacks and nearly a 100% success rate for non-targeted attacks with only 1–2 queries per image.

System fragility analysis of highway bridge using multi-output Gaussian process regression surrogate model

This study presents a multi-output Gaussian process regression (GPR) surrogate model for seismic-fragility analysis of bridge structural systems. Multi-output GPR can model the correlations among multiple outputs, accuracy and stability are achieved with fewer training data, which reduces the computational cost of fragility analysis. Furthermore, the explainability of the constructed surrogate model is implemented by adopting an automatic relevance-determination (ARD) kernel in the GPR. The estimated hyperparameters can provide the contribution of the uncertainty of each input parameter to the outputs. The fragility analysis using the multi-output GPR surrogate model was verified by applying it to a seismic isolation highway bridge with multiple spans and a curved geometry. The effectiveness of the multi-output GPR was demonstrated by the construction of an accurate and stable surrogate model with 46 inputs and 28 outputs. The relative contributions of the uncertainties to the structural properties and input earthquake loads could also be understood. The fragility curves, at both the component and system levels, were appropriately obtained using a sufficient number of samples in a Monte Carlo calculation. Furthermore, the failure modes were evaluated, identifying which structural components contributed to the system failure. This enabled discussions on structural system failures from the viewpoint of the structural dynamic characteristics of the bridge and earthquake-load properties.

Enhanced Drag Force Estimation in Automotive Design: A Surrogate Model Leveraging Limited Full-Order Model Drag Data and Comprehensive Physical Field Integration

In this paper, a novel surrogate model for shape-parametrized vehicle drag force prediction is proposed. It is assumed that only a limited dataset of high-fidelity CFD results is available, typically less than ten high-fidelity CFD solutions for different shape samples. The idea is to take advantage not only of the drag coefficients but also physical fields such as velocity, pressure, and kinetic energy evaluated on a cutting plane in the wake of the vehicle and perpendicular to the road. This additional “augmented” information provides a more accurate and robust prediction of the drag force compared to a standard surface response methodology. As a first step, an original reparametrization of the shape based on combination coefficients of shape principal components is proposed, leading to a low-dimensional representation of the shape space. The second step consists in determining principal components of the x-direction momentum flux through a cutting plane behind the car. The final step is to find the mapping between the reduced shape description and the momentum flux formula to achieve an accurate drag estimation. The resulting surrogate model is a space-parameter separated representation with shape principal component coefficients and spatial modes dedicated to drag-force evaluation. The algorithm can deal with shapes of variable mesh by using an optimal transport procedure that interpolates the fields on a shared reference mesh. The Machine Learning algorithm is challenged on a car concept with a three-dimensional shape design space. With only two well-chosen samples, the numerical algorithm is able to return a drag surrogate model with reasonable uniform error over the validation dataset. An incremental learning approach involving additional high-fidelity computations is also proposed. The leading algorithm is shown to improve the model accuracy. The study also shows the sensitivity of the results with respect to the initial experimental design. As feedback, we discuss and suggest what appear to be the correct choices of experimental designs for the best results.