AeroJEPA: Scalable 3D Aerodynamic Modeling

• AeroJEPA is a joint-embedding predictive architecture that transforms complex CFD outputs into low-dimensional latent tokens for efficient surrogate modeling.
• It employs a transformer-based latent predictor and a continuous implicit decoder to reconstruct 3D aerodynamic fields at arbitrary resolutions with reduced computational cost.
• Benchmarks on HiLiftAeroML and SuperWing demonstrate lower relative L₂ errors and uniform inference efficiency compared to traditional chunk-wise CFD methods.

AeroJEPA is a Joint-Embedding Predictive Architecture for scalable 3D aerodynamic field modeling that decouples surrogate model prediction from full computational fluid dynamics (CFD) field resolution. Rather than directly mapping input geometries to high-dimensional CFD outputs, AeroJEPA operates by learning low-dimensional latent representations ("tokens") of both geometric context and target flow, bridges them via a predictive latent regressor, and reconstructs physical fields as needed through an implicit neural representation (INR). This architecture enables efficient surrogate modeling of extremely large aerodynamic fields, while producing semantically meaningful latent spaces useful for design and analysis (Giral et al., 7 May 2026).

1. Architectural Overview

AeroJEPA's central premise is to replace direct field regression with a latent-to-latent prediction pipeline, separating the encoding of input geometry plus operating conditions from the encoding of ground-truth CFD outputs. Training objective is then cast as a token-level matching in latent space, with optional field-level supervision via an INR decoder.

Context Latent Representation

• Input: Unstructured point cloud of solid boundary, $$\mathcal{P} = \{x_i \in \partial\Omega\}_{i=1}^{N_c}$$
• Subsampling: Farthest Point Sampling (FPS) to $N_c \sim 8\times10^3$–$1.3\times10^5$ points
• Encoder: Composition of centroid clustering, local message passing, and Point-Transformer blocks
• Output: $$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$, where $M$ = token count, $d$ = token dimension (dataset-dependent)

Target Latent Representation

• Input: Independently subsampled point cloud of CFD outputs, $\mathcal{F} = \{(q_j, \phi(q_j))\}_{j=1}^{N_t}$
• Encoder: $\mathcal{E}_t$, with structure analogous to context encoder
• Output: $$Z_t = \mathcal{E}_t(\mathcal{F}) \in \mathbb{R}^{M\times d}$$ (used only at training time)

Latent Predictor

• Structure: Transformer-style network $f_\theta^{\mathrm{pred}}$ with alternating self-attention, cross-attention, MLP mixing, FiLM-style conditioning on operating variables $N_c \sim 8\times10^3$0 in every layer
• Operation: $N_c \sim 8\times10^3$1 produces predicted flow tokens
• Loss: Token-wise latent-matching,

$N_c \sim 8\times10^3$2

2. Continuous Implicit Decoder

AeroJEPA leverages a continuous INR decoder $N_c \sim 8\times10^3$3 to reconstruct physical fields from predicted latent tokens at arbitrary spatial resolution. This MLP-based decoder accepts each query point $N_c \sim 8\times10^3$4 (optionally with signed distance function) and the latent code $N_c \sim 8\times10^3$5, and outputs field values such as velocity $N_c \sim 8\times10^3$6 and pressure $N_c \sim 8\times10^3$7:

$N_c \sim 8\times10^3$8

Internally, query coordinates are lifted using Fourier features and pooled with learned summaries or attended token subsets before entering the MLP, effectively decoupling output cost from field discretization and supporting continuous-domain inference.

3. Training Objectives and Regularization

Full end-to-end training minimizes a composite loss:

$N_c \sim 8\times10^3$9

Terms are:

• $1.3\times10^5$0: Latent-matching loss, as above
• $1.3\times10^5$1: Reconstruction loss,

$1.3\times10^5$2

• $1.3\times10^5$3: SIGReg regularization, which enforces token diversity by urging random projections toward isotropic Gaussian
• Typical weights: $1.3\times10^5$4, $1.3\times10^5$5, $1.3\times10^5$6

A "latent-only" second training phase drops the reconstruction loss, optimizing only latent-level objectives.

The learning process is summarized by the following pseudo-code sketch:

$d$9

4. Benchmark Datasets and Comparative Results

AeroJEPA is evaluated on realistic, large-scale benchmarks designed to test aerodynamic surrogate performance.

HiLiftAeroML

• WMLES for high-lift aircraft; surface boundary layer $1.3\times10^5$7–$1.3\times10^5$8M points, volumetric domain $1.3\times10^5$9M points
• 8 geometric control parameters, 205 training/50 test geometries, each at 10 angles of attack (AoA)
• $$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$0, $$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$1; per-baseline chunk size $$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$2k points vs. single-latent decode in AeroJEPA

Field	AeroJEPA (Rel L₂)	Best Baseline (Rel L₂)	Inference TFLOPs
$$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$3	0.0048 ± 0.0026	0.0206 ± 0.0047 (FigConvUNet)	57 vs. 88
$$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$4	0.1445 ± 0.0423	0.4761 ± 0.0934	57 vs. 88
$$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$5	0.2749 ± 0.0388	0.8492 ± 0.0555	57 vs. 88
$$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$6	0.1880 ± 0.0455	0.7137 ± 0.0864	57 vs. 88

AeroJEPA achieves lower relative $$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$7 error for all fields and requires fewer inference FLOPs due to the single latent-based decode, whereas baselines operate chunk-wise, incurring significant overhead.

SuperWing

• $$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$8 transonic wings $$Z_c = \mathcal{E}_c(\mathcal{P}) \in \mathbb{R}^{M\times d}$$9 RANS snapshots; 54 morphological parameters; fixed grid $M$0k points
• $M$1, $M$2; AeroJEPA is independent of inference chunking

Field	Chunked Best	One-pass Best	AeroJEPA
$M$3	0.1429	0.0280	0.0548
$M$4	0.2912	0.0529	0.1084
$M$5	0.1946	0.0309	0.0644

AeroJEPA maintains competitive accuracy and uniform computational cost per inference ($M$6 TFLOPs), regardless of output resolution, compared with baselines requiring chunked or single-pass decoding at greater expense.

5. Latent Space Semantics and Analysis

The semantically structured latent space induced by AeroJEPA supports a spectrum of analysis and design utilities beyond field regression.

Linear Probing

Ridge regression probes of standardized mean-pooled latents ($M$7) uncover direct mapping to design variables and aerodynamic properties:

• On HiLiftAeroML, context latents predict flap and slat deflections with $M$8; predicted latents recover $M$9 and $d$0 to $d$1, $d$2 respectively.
• On SuperWing, predicted latents yield $d$3, $d$4; context latents retrieve 9/54 morphological parameters at $d$5.

Controlled Latent Interpolation

Linear interpolation between two predicted latents,

$d$6

generates physically plausible intermediate CFD fields whose macroscopic coefficients track the dataset ground truth, supporting meaningful field morphing.

Concept-Vector Arithmetic

Probing geometric parameters defines orthogonal concept subspaces; walks along these axes in latent space shift design variables independently in accordance with physical aircraft practice, as demonstrated by the near block-diagonal structure of the HiLift deflection-response matrix.

Constrained Latent-Space Optimization

Treating $d$7 as a design variable, direct optimization for maximum $d$8 is possible under Mahalanobis trust regions, parameter bounds, and physical constraints. Optimization converges to solutions coincident with the empirical design frontier. Gradient-based search is executed using SLSQP and autograd-computed Jacobians.

6. Significance and Implications

AeroJEPA demonstrates the feasibility of predictive latent learning for aerodynamic surrogate modeling at realistic, field-scale resolutions. Its capacity for single-shot, mesh-size-invariant inference, explicit regularization vs. token collapse, and emergence of semantically organized latent spaces enables not only accurate field prediction but downstream physical analysis and gradient-based design. A plausible implication is that such architectures may generalize to other domains exhibiting large-scale physical field structure, where latent-pathway surrogates are desired for analysis-aware modeling and automated inverse design (Giral et al., 7 May 2026).