Technical Summary: AeroJEPA

Problem Statement

Aerodynamic design increasingly relies on "many-query" regimes where engineers must repeatedly evaluate high-dimensional flow fields across vast spaces of geometries and operating conditions. While high-fidelity Computational Fluid Dynamics (CFD) remains the gold standard, its computational cost prohibits direct optimization and rapid iteration. Existing neural surrogate models attempt to address this but face two critical limitations in realistic 3D aerodynamics:

1. Scalability: Many approaches are optimized for direct field prediction on fixed discretizations, making them difficult to scale to the massive output sizes (e.g., tens of millions of points) found in high-fidelity boundary-layer simulations.
2. Lack of Semantic Structure: Even accurate models often fail to produce latent representations that are directly useful for analysis or design. They predict fields but do not yield latent variables clearly aligned with geometry, operating conditions, or underlying physics, hindering their utility for scientific understanding and gradient-based design optimization.

Methodology: AeroJEPA

The authors introduce AeroJEPA, a Joint-Embedding Predictive Architecture tailored for 3D aerodynamic field modeling. Unlike traditional surrogates that map geometry directly to high-dimensional flow fields or autoencoders that focus on pixel/voxel reconstruction, AeroJEPA operates within a learned, physically meaningful latent space.

Core Architecture

The framework decouples geometry encoding, latent prediction, and field decoding through a tokenized interface:

• Context Encoder ($E_c$): Maps the geometric design (represented as an unstructured point cloud of boundary condition points) and operating conditions (e.g., angle of attack, Reynolds number, Mach number) into a fixed-size set of context tokens ($Z_c$).
• Target Encoder ($E_t$): Used only during training, this maps the ground-truth fluid field (subsampled independently from the geometry) into target tokens ($Z_t$).
• Predictor ($f^{pred}_\theta$): Instead of predicting the dense field directly, the predictor operates entirely in the tokenized latent space. It takes the context tokens ($Z_c$) and operating conditions ($c$) to predict the target flow tokens ($\hat{Z}_t$). This formulation learns the map from geometry-conditioned tokens to flow-conditioned tokens.
• Implicit Neural Representation (INR) Decoder ($f^{dec}_\phi$): An optional continuous decoder that reconstructs the physical fluid field (velocity, pressure) at arbitrary spatial query points $q$ from the predicted latent state $\hat{Z}_t$. This allows for resolution-independent output without requiring volumetric meshing.

Training Objectives

AeroJEPA employs a coupled training workflow to avoid representation collapse while ensuring physical validity:

• Latent Matching Loss ($L_{lat}$): Aligns the predicted tokens ($\hat{Z}_t$) with the target tokens ($Z_t$) token-by-token.
• Reconstruction Loss ($L_{rec}$): When the decoder is included, it minimizes the error between the decoded field and the ground truth at sampled query points.
• SIGReg Regularization ($L_{sig}$): An explicit regularizer applied to the latent distribution to prevent collapse and encourage a well-spread embedding space, replacing the need for Exponential Moving Average (EMA) teachers or stop-gradient heuristics.

The total loss is a weighted sum: $L_{total} = \lambda_\ell L_{lat} + \lambda_r L_{rec} + \lambda_s L_{sig}$.

Key Contributions

1. JEPA-Style Predictive Latent Architecture: The paper formulates a novel surrogate modeling approach that combines geometry-conditioned latent prediction with a continuous INR decoder, moving the expensive learning problem from dense field prediction to structured latent prediction.
2. Semantically Meaningful Latent Spaces: The authors demonstrate that the learned latent spaces are not merely descriptive but structurally aligned with design variables and aerodynamic quantities. Despite not being trained on integrated coefficients (like $C_L$ or $C_D$) or specific design parameters, these quantities can be linearly recovered from the latent space with high fidelity.
3. Scalability and Optimization Utility: The approach is shown to be competitive for field prediction while naturally scaling to high-resolution outputs. Furthermore, the smooth latent structure enables a lightweight, differentiable optimization workflow in latent space, bypassing the need for repeated mesh manipulation or full-field decoding during the optimization loop.

Experimental Results

The method was evaluated on two complementary datasets: HiLiftAeroML (high-fidelity, large-scale boundary-layer fields on realistic high-lift aircraft) and SuperWing (broad generalization over a parametric family of transonic wings).

• Surrogate Accuracy: On HiLiftAeroML, AeroJEPA outperformed baseline models (FigConvUNet, GeoTransolver, Transolver) in relative $L_2$ and $L_1$ errors for pressure and velocity fields while requiring significantly lower inference computational cost (e.g., ~57 TFLOPs vs. ~88–309 TFLOPs for baselines). It successfully captured complex separated-flow structures on unseen configurations.
• Latent Structure:
  • Probing: Linear probes recovered high-lift control-surface deflections from context latents with $R^2$ values between 0.965 and 0.988, and aerodynamic coefficients ($C_L, C_D$) from predicted latents with $R^2$ of 0.930 and 0.996, respectively.
  • Interpolation & Arithmetic: The latent space supported controlled interpolation between operating conditions and geometry states. Concept-vector arithmetic revealed that flap and slat controls were nearly disentangled (orthogonal subspaces), while inboard/outboard segments of the same surface showed expected physical coupling.
• Optimization: On SuperWing, the authors performed a proof-of-concept optimization to maximize aerodynamic efficiency ($C_L/C_D$) directly in the 128-dimensional context latent space. The search converged to a design point corresponding to a high-efficiency wing configuration (large aspect ratio, high sweep) that existed within the dataset's envelope, demonstrating the latent space's utility for design exploration.

Significance and Claims

The paper posits that predictive latent learning is a promising direction for aerodynamic surrogate modeling. The significance of AeroJEPA lies in its ability to provide surrogates that are not only scalable and accurate but also analyzable and useful for design-space exploration. By decoupling prediction from spatial resolution and organizing the latent space semantically, the method enables rapid design cycles and controlled traversal of the design space without the computational overhead of repeated high-fidelity CFD evaluations.

The authors maintain a modest stance, noting that the current study is limited to two datasets and primarily steady-flow regimes. The optimization and latent analyses are presented as proof-of-concept demonstrations of semantic structure rather than a complete, end-to-end industrial design pipeline. Future work is identified as necessary to address broader flow regimes, tighter integration with inverse design pipelines, and unsteady or multi-fidelity settings.