Rodrigo Castellanos

Víctor Francés-Belda, Alberto Solera-Rico, Javier Nieto-Centenero et al.

Surrogate models that combine dimensionality reduction and regression techniques are essential to reduce the need for costly high-fidelity computational fluid dynamics data. New approaches using $β$-Variational Autoencoder ($β$-VAE) architectures have shown promise in obtaining high-quality low-dimensional representations of high-dimensional flow data while enabling physical interpretation of their latent spaces. We propose a surrogate model based on latent space regression to predict pressure distributions on a transonic wing given the flight conditions: Mach number and angle of attack. The $β$-VAE model, enhanced with Principal Component Analysis (PCA), maps high-dimensional data to a low-dimensional latent space, showing a direct correlation with flight conditions. Regularization through $β$ requires careful tuning to improve overall performance, while PCA preprocessing helps to construct an effective latent space, improving autoencoder training and performance. Gaussian Process Regression is used to predict latent space variables from flight conditions, showing robust behavior independent of $β$, and the decoder reconstructs the high-dimensional pressure field data. This pipeline provides insight into unexplored flight conditions. Furthermore, a fine-tuning process of the decoder further refines the model, reducing the dependence on $β$ and enhancing accuracy. Structured latent space, robust regression performance, and significant improvements in fine-tuning collectively create a highly accurate and efficient surrogate model. Our methodology demonstrates the effectiveness of $β$-VAEs for aerodynamic surrogate modeling, offering a rapid, cost-effective, and reliable alternative for aerodynamic data prediction.

Víctor Francés-Belda, Carlos Sanmiguel Vila, Rodrigo Castellanos

Accurate and efficient surrogate models for aerodynamic surface pressure fields are essential for accelerating aircraft design and analysis, yet deterministic regressors trained with pointwise losses often smooth sharp nonlinear features. This work presents a conditional denoising diffusion probabilistic model for predicting surface pressure distributions on the NASA Common Research Model wing under varying conditions of Mach number, angle of attack, and four control surface deflections. The framework operates on unstructured surface data through a principal component representation used as a non-truncated, reversible linear reparameterization of the pressure field, enabling a fully connected architecture. A signal-aware training objective is derived by propagating a reconstruction loss through the diffusion process, yielding a timestep-dependent weighting that improves fidelity in regions with strong pressure gradients. The stochastic sampling process is analyzed through repeated conditional generations, and two diagnostic metrics are introduced, the Local Reliability Index and Global Reliability Index, to relate sampling-induced spread to reconstruction error. Relative to the considered deterministic baselines, the proposed formulation reduces mean absolute error and improves the reconstruction of suction peaks, shock structures, and control surface discontinuities. The sampling-induced spread exhibits strong correspondence with surrogate error, supporting its interpretation as a qualitative reliability indicator rather than calibrated uncertainty quantification.

Isaac Robledo, Alberto Vilariño, Arnau Miró et al.

Active multi-fidelity surrogate modeling is developed for multi-condition airfoil shape optimization to reduce high-fidelity CFD cost while retaining RANS-level accuracy. The framework couples a low-fidelity-informed Gaussian process regression transfer model with uncertainty-triggered sampling and a synchronized elitism rule embedded in a hybrid genetic algorithm. Low-fidelity XFOIL evaluations provide inexpensive features, while sparse RANS simulations are adaptively allocated when predictive uncertainty exceeds a threshold; elite candidates are mandatorily validated at high fidelity, and the population is re-evaluated to prevent evolutionary selection based on outdated fitness values produced by earlier surrogate states. The method is demonstrated for a two-point problem at $Re=6\times10^6$ with cruise at $α=2^\circ$ (maximize $E=L/D$) and take-off at $α=10^\circ$ (maximize $C_L$) using a 12-parameter CST representation. Independent multi-fidelity surrogates per flight condition enable decoupled refinement. The optimized design improves cruise efficiency by 41.05% and take-off lift by 20.75% relative to the best first-generation individual. Over the full campaign, only 14.78% (cruise) and 9.5% (take-off) of evaluated individuals require RANS, indicating a substantial reduction in high-fidelity usage while maintaining consistent multi-point performance.

Javier Nieto-Centenero, Esther Andrés, Rodrigo Castellanos

Accurate aerodynamic prediction often relies on high-fidelity simulations; however, their prohibitive computational costs severely limit their applicability in data-driven modeling. This limitation motivates the development of multi-fidelity strategies that leverage inexpensive low-fidelity information without compromising accuracy. Addressing this challenge, this work presents a multi-fidelity deep learning framework that combines autoencoder-based transfer learning with a newly developed Multi-Split Conformal Prediction (MSCP) strategy to achieve uncertainty-aware aerodynamic data fusion under extreme data scarcity. The methodology leverages abundant Low-Fidelity (LF) data to learn a compact latent physics representation, which acts as a frozen knowledge base for a decoder that is subsequently fine-tuned using scarce HF samples. Tested on surface-pressure distributions for NACA airfoils (2D) and a transonic wing (3D) databases, the model successfully corrects LF deviations and achieves high-accuracy pressure predictions using minimal HF training data. Furthermore, the MSCP framework produces robust, actionable uncertainty bands with pointwise coverage exceeding 95%. By combining extreme data efficiency with uncertainty quantification, this work offers a scalable and reliable solution for aerodynamic regression in data-scarce environments.