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D-JEPA: Design-Recoverable JEPA Representation with Swappable Physics Decoders

Nitin Nagesh Kulkarni, Aashwin Anand Mishra, Yin Yu, Peter Lyu

arXiv:2609.33110v1cs.LGcs.AI

TL;DR

Parameterized physical surrogates may entangle geometry with conditions and response tasks, limiting reuse. D-JEPA encodes geometry alone, pairs it with lightweight physics-specific decoders, and encourages design-variable recovery. Across three 3D aerodynamic benchmarks, it maintains or improves full-field accuracy, with further evaluation of reuse, transfer, and CFD-validated design optimization.

  • Problem

    AeroDB construction spans costly geometry–condition combinations, while response-specific surrogates do not necessarily yield representations reusable across conditions or quantities of interest.

    Source: §1 · pp. 1–2

  • Method

    D-JEPA encodes geometry into a compact latent without conditions or target physics, uses lightweight physics-specific decoders, and encourages design-variable recoverability.

    Source: §1 · p. 2, §2.1 · p. 3

  • Results

    Across three challenging parameterized 3D aerodynamic benchmarks, D-JEPA maintains or improves full-field surrogate accuracy and maintains high integral aerodynamic accuracy.

    Source: §4 · p. 9

  • Takeaways & Limitations

    Design-variable recovery provides a differentiable path from physical objectives to design parameters for gradient-based design exploration.

    Source: §3.4 · p. 9

    Evaluation covers a small set of aerodynamic and structural benchmarks, and physics transfer is demonstrated only from CFD to structural response.

    Source: §3.4 · p. 9

Abstract

from arXiv · show

Joint-Embedding Predictive Architectures (JEPAs) provide a framework for learning compact representations without directly reconstructing high-dimensional observations. However, in parameterized physical systems, learned representations can entangle geometry with operating conditions and task-specific physical responses, limiting their reuse across prediction tasks. We introduce D-JEPA (Design-recoverable JEPA), a geometry-centric JEPA that computes a compact representation from geometry alone and reuses it across operating conditions and physical response spaces through lightweight physics-specific decoders. An explicit design-recoverability objective encourages the geometry latent to preserve information about the underlying design variables, enabling the representation to support design analysis and optimization. We further identify a case-level collapse failure mode in which target representations become nearly invariant across distinct geometries despite low reconstruction error, and mitigate it using case-level variation constraints and auxiliary target reconstruction. Across four 3D aerodynamic, hydrodynamic, and structural benchmarks, D-JEPA maintains or improves full-field prediction accuracy while achieving near-perfect linear recoverability of design parameters. The frozen geometry representation can be reused at held-out operating conditions and transferred to a structural response task with fewer trainable parameters. Finally, the representation supports differentiable design optimization, with designs validated using high-fidelity CFD, preserving the predicted ranking of candidate designs. These results demonstrate that separating a reusable geometry representation from physics-specific prediction provides a practical representation for scientific surrogate modeling and design.

1 INTRODUCTION

D-JEPA separates geometry representation from condition- and physics-specific prediction, while explicitly encouraging recovery of design variables. The paper frames this reusable representation as a response to expensive simulation and limited reuse across prediction tasks.

1 INTRODUCTION

  • High-fidelity CFD makes AeroDB population prohibitively expensive across combinatorial geometry and operating-condition spaces, motivating reusable geometry representations for downstream physical predictions and design tasks.Source: §1 · pp. 1–2
  • JEPA learns predictive relationships between compact latent representations, but a representation entangled with conditions or physical responses may be difficult to reuse across tasks.The paper poses geometry-only representation independent of operating conditions and physical response as an open question.Source: §1 · p. 2
  • D-JEPA encodes each geometry into a compact latent and conditions lightweight physics decoders on operating conditions.The geometry encoder receives neither operating conditions nor target physics.Source: §1 · p. 2
  • An explicit design-recoverability objective encourages the geometry latent to preserve design-variable information recoverable through a shallow probe.Source: §1 · p. 2
  • The shared geometry encoder can be reused across operating conditions and physical response spaces while lightweight physics-specific decoders are swapped without retraining it.Source: §1 · p. 2
  • The evaluation covers parameterized aerodynamic benchmarks, operating-condition reuse, cross-physics transfer, and differentiable design optimization validated with high-fidelity CFD.Source: §1 · p. 2

2 METHOD

D-JEPA separates a geometry-only latent from operating-condition- and physics-specific prediction, then shapes that latent to preserve design information. Its method combines coordinate-aware geometry encoding, implicit physics decoders, and training constraints intended to maintain variation across design cases.

2.1 PROBLEM FORMULATION

  • The geometry encoder maps a parameterized surface to a compact latent, while operating conditions and physics regimes enter through downstream decoders.The design vector supervises an auxiliary recoverability objective rather than serving as a physics-decoder input.Source: §2.1 · p. 3

2.2 D-JEPA FRAMEWORK

  • The JEPA pathway predicts target tokens from geometry and conditions, while the physics decoder directly predicts fields at query locations.The target encoder is used during training; the latent prediction loss shapes the representation, whereas field reconstruction evaluates its prediction utility.Source: §2.2 · p. 3

2.3 COORDINATE-AWARE GEOMETRY ENCODING

  • Coordinate-aware encoding concatenates learned local point features with global and regional geometric descriptors before mapping them to the geometry latent.The global descriptor summarizes scale, extent, and spatial distribution; the regional descriptor uses statistics from a 5 × 5 × 5 voxel grid.Source: §2.3 · pp. 3–4

2.4 FILM-MODULATED IMPLICIT NEURAL FIELD DECODER

  • Each physics-specific implicit decoder combines the geometry latent with query location, surface normal, and operating condition to predict a local field.FiLM modulates four residual blocks, and automatic differentiation provides surrogate gradients with respect to the latent and design variables without a separate PDE-adjoint computation.Source: §2.4 · p. 4

2.5 TRAINING OBJECTIVES AND DESIGN RECOVERABILITY

  • Training jointly uses latent prediction, field reconstruction, and design recoverability so the geometry latent is explicitly encouraged to retain design information.Design parameters supervise the representation through the recoverability loss and are not supplied to the physics decoder.Source: §2.5 · p. 5

2.6 PREVENTING REPRESENTATION COLLAPSE

  • Case-level SIGReg, across-design variance constraints, and auxiliary target reconstruction address representations that vary across tokens but remain nearly constant across geometries.Together, the constraints increase observed between-case standard deviation from approximately 0.0032 to approximately 1.0 across evaluated datasets.Source: §2.6 · p. 5

2.7 PHYSICS DECODER TRANSFER

  • For transfer to a new physical response space, the geometry encoder is frozen and a new physics decoder is trained without propagating gradients through the encoder.The experiment tests whether the fixed latent captures geometric information reusable by a new decoder.Source: §2.7 · p. 5

3 RESULTS & DISCUSSION

Across four 3D aerodynamic, hydrodynamic, and structural benchmarks, D-JEPA is evaluated for full-field prediction and reusable geometry representations. Results cover case-level variation, design-variable recovery, operating-condition reuse, cross-physics transfer, and CFD-validated design optimization.

3.1 EXPERIMENTAL DATASETS

  • The four benchmarks span aircraft wings, submarine hulls, automotive geometries, and coupled fluid–structure interaction for automotive hoods.The evaluation includes full-field and integrated prediction, representation reuse, transfer to new response spaces, and design optimization.Source: §3.1 · p. 6, §3 · p. 6

3.2 FULL-FIELD SURROGATE ACCURACY

  • R2 = 0.9971 (SHIFT-Wing), 0.9967 (SHIFT-Submarine), and 0.9937 (SHIFT-SUV) for surface pressure; D-JEPA maintained or improved full-field accuracy versus AeroJEPA.It also improved SHIFT-Wing CD from R2 = 0.973 to 0.990 and CL from 0.952 to 0.970.Source: §3.2 · p. 6

3.3.1 PREVENTING CASE-LEVEL REPRESENTATION COLLAPSE

  • Between-case target-representation standard deviation rises from 0.0002–0.0004 without case-level constraints to about 1.0 with the variance hinge and target reconstruction.Token-level SIGReg alone produces essentially no change; pressure prediction changes only modestly.Source: Table 2 · p. 7, §3.3.1 · p. 7

3.3.2 DESIGN-VARIABLE RECOVERABILITY

  • Mean linear-probe R2 reaches 0.989 (SHIFT-SUV), 0.998 (SHIFT-Wing), and 0.998 (SHIFT-Submarine), versus AeroJEPA's 0.683, 0.801, and 0.882, respectively.Removing the design loss substantially reduces design recovery, with a comparatively smaller effect on pressure prediction.Source: §3.3.2 · p. 7

3.3.3 OPERATING-CONDITION SWEEPS (SAME PHYSICS, NEW CONDITIONS)

  • R2 = 0.9922 and 0.9944 at held-out Mach numbers 0.7750 and 0.8125, respectively, using one frozen geometry representation for interpolation within the trained range.Across all evaluated Mach conditions, pressure prediction remains at R2 ≥ 0.9902.Source: §3.3.3 · pp. 7–8, Table 4 · p. 8

3.3.4 SWAPPABLE PHYSICS DECODERS (CROSS-PHYSICS TRANSFER)

  • A frozen aerodynamic encoder with 0.56 M trainable parameters reaches structural-displacement R2 = 0.3316 after 10 epochs, versus 0.0396 from scratch using 2.30 M parameters.The transferred model remains ahead through 300 epochs, when the approaches are within 0.007 of each other.Source: §3.3.4 · p. 8, Table 5 · p. 9

3.4 DESIGN OPTIMIZATION & CFD VALIDATION

  • Predicted and CFD rankings match for all four candidates on SHIFT-Submarine drag and SHIFT-Wing lift, including extrapolative OPT-Wide.SHIFT-Submarine predicted drag agrees with CFD within 0.6–2.0%; SHIFT-Wing relative lift error ranges from 0.72–10.74%.Source: §3.4 · pp. 8–9, Table 6 · p. 9
  • Evaluation remains limited to a small set of aerodynamic and structural benchmarks; transfer is demonstrated only from CFD to structure, and optimization uses differentiable surrogates with predefined objectives.High-fidelity CFD validation was unavailable for SHIFT-SUV because the setup and sufficient geometry and operating-condition information were unavailable.Source: §3.4 · pp. 8–9

4 CONCLUSIONS

D-JEPA separates reusable geometric information from physics- and condition-specific prediction. Across three aerodynamic benchmarks it maintains or improves full-field accuracy, and the representation is reused across geometry families and conditions, transferred to structural prediction, and used in validated design optimization.

4 CONCLUSIONS

  • Across three 3D aerodynamic benchmarks, D-JEPA maintains or improves full-field surrogate accuracy relative to evaluated baselines while retaining high accuracy for integral aerodynamic quantities.The representation is reused across geometry families and operating conditions, transferred to AutoHood 3D structural response without retraining the geometry encoder, and used for gradient-based design optimization with candidates validated against high-fidelity CFD.Source: §4 · p. 9

APPENDIX

  • The appendix provides implementation and evaluation details intended to support reproduction of the main-paper experiments.Its coverage includes dataset construction, architecture, training objectives, collapse diagnostics, evaluation protocols, transfer, optimization, and computational requirements.Source: APPENDIX · p. 13

A DATASET SPECIFICATIONS AND PREPROCESSING PIPELINES

The benchmarks represent parameterized 3D physical systems using point clouds, surface normals, solver-generated fields, design parameters, and applicable operating conditions. The dataset set spans aerodynamic, hydrodynamic, and structural response settings.

A DATASET SPECIFICATIONS AND PREPROCESSING PIPELINES

  • Four benchmarks—SHIFT-Wing, SHIFT-Submarine, SHIFT-SUV, and AutoHood 3D—span parameterized 3D physical systems with geometry, surface normals, solver-generated fields, design parameters, and applicable operating conditions.Table A.1 summarizes benchmark characteristics.Source: A DATASET SPECIFICATIONS AND… · p. 13, Table A.1 · p. 13
  • The explicit design parameters train the design-recoverability objective but are not direct physics-decoder inputs; inference uses geometry representation, query location, local normal, and operating conditions.The separation makes design variables information to be recovered from the representation rather than decoder inputs.Source: A DATASET SPECIFICATIONS AND… · p. 13
  • AutoHood 3D tests reuse of one geometry representation for aerodynamic pressure and structural displacement, while SHIFT-Wing tests conditioning across Mach number and angle of attack.SHIFT-Submarine and SHIFT-SUV use fixed flow conditions, so their operating-condition vectors are empty.Source: A DATASET SPECIFICATIONS AND… · p. 13

B DETAILED MODEL ARCHITECTURE

D-JEPA builds a geometry-only representation from point clouds and normals, augments local features with geometric descriptors, and uses a JEPA pathway to shape that representation. A separate FiLM-modulated physics decoder maps it to response fields and can be replaced while keeping the encoder fixed.

B.1 GEOMETRY ENCODER

  • The geometry encoder processes an unstructured point cloud and surface normals into 512 context tokens of dimension 128, using local neighborhoods and a six-block transformer before mean-and-maximum pooling.The neighborhood sizes are 16 for message passing and 16 for local attention; the transformer has eight attention heads and an MLP expansion factor of four.Source: §B.1 · pp. 13–14

B.2 GLOBAL AND REGIONAL GEOMETRIC DESCRIPTORS

  • The final 128-dimensional geometry representation combines token features with global and regional geometric descriptors, without operating-condition or physics identifiers as encoder inputs.Global statistics include coordinate and bounding-box measures; regional features use a 5 × 5 × 5 voxel grid with 1,625 features.Source: §B.2 · p. 14, §B.1 · p. 14

B.3 JEPA REPRESENTATION-LEARNING PATHWAY

  • The JEPA pathway predicts target latent tokens from a context representation to shape the geometry representation, while the physics-field decoder receives the geometry representation directly.The JEPA predictor is not the physics-field decoder, keeping representation learning distinct from physical output mapping.Source: §B.3 · p. 14

B.4 FILM-MODULATED PHYSICS DECODER

  • For each physical response space, a FiLM-modulated decoder maps geometry representation, query location, and operating condition to the predicted field, allowing a new decoder to be trained with the encoder fixed.Geometry modulates the query pathway through learned affine scale and shift parameters; aerodynamic outputs include pressure and three wall-shear-stress components.Source: §B.4 · p. 14

C.1 COMPOSITE TRAINING OBJECTIVE

D-JEPA combines latent prediction, physical reconstruction, design-variable recovery, representation regularization, and target reconstruction. The optimization schedule uses matched settings for AeroJEPA and D-JEPA unless specified otherwise.

C.1 COMPOSITE TRAINING OBJECTIVE

  • The composite objective combines latent prediction and physical reconstruction with design recovery, token- and case-level regularization, variance constraints, and target reconstruction.Case-level regularization and variance constraints address variation across geometry cases, while target reconstruction connects target representations to local physical coordinates.Source: §C.1 · pp. 14–15

C.2 OPTIMIZATION SCHEDULE

  • AeroJEPA and D-JEPA use matched optimization settings unless otherwise specified, with batch size 16 for SHIFT-Wing, SHIFT-SUV, and SHIFT-Submarine to accommodate solver-mesh memory requirements.The optimization configuration and training hyperparameters are summarized in Table A.3.Source: §C.2 · p. 15, Table A.3 · p. 15

D REPRESENTATION-COLLAPSE DIAGNOSTICS

The diagnostic measures variation in target representations across geometry cases, distinguishing it from token diversity within a case. Near-zero case-level variation can coexist with low latent loss and modest changes in downstream metrics, so it should be monitored directly.

D REPRESENTATION-COLLAPSE DIAGNOSTICS

E EVALUATION PROTOCOLS

The evaluation uses held-out geometry cases, fixed validation partitions, and three training seeds to assess field prediction, integrated forces, and design-variable recovery.

E EVALUATION PROTOCOLS

  • Validation uses fixed 10% partitions and held-out geometry cases, with uncertainty reported as standard deviations across three independent training seeds.Source: E EVALUATION PROTOCOLS · p. 16
  • Field accuracy is the coefficient of determination R2 computed per physical output variable and averaged across held-out cases; integrated drag and lift are directly integrated from predicted pressure and wall-shear fields.No secondary regression head predicts the integrated quantities.Source: E EVALUATION PROTOCOLS · p. 16
  • Design-variable recovery uses a standardized five-fold cross-validated ridge probe on frozen 128-dimensional geometry representations, with out-of-fold R2 reported.Source: E EVALUATION PROTOCOLS · p. 16
  • Qualitative field comparisons use dense high-resolution solver meshes and show representative median and worst-case held-out examples.Source: E EVALUATION PROTOCOLS · p. 16

F BASELINE MODELS AND COMPARATIVE BENCHMARKS

The appendix describes AeroJEPA as the primary representation-learning baseline and evaluates GeoTransolver and DoMINO using official implementations on the same dataset splits. Field and integrated-force comparisons are reported in the main-text table, while appendix figures provide qualitative AeroJEPA pressure predictions.

F.1 AEROJEPA BASELINE

  • AeroJEPA is the primary representation-learning baseline, with shared backbone components, point sampling, optimizer settings, and reconstruction objective where applicable.Its pooled 128-dimensional context representation is probed using the same linear procedure as D-JEPA.Source: §F.1 · pp. 16–17
  • Figures A.1–A.3 show predicted pressure and absolute point-wise error for median and worst-case held-out geometries across SHIFT-SUV, SHIFT-Submarine, and SHIFT-Wing.Source: Figure A.1 · p. 17, Figure A.2 · p. 17, Figure A.3 · p. 18

F.2 GEOTRANSOLVER AND DOMINO BASELINES

  • GeoTransolver and DoMINO are evaluated with their official implementations on the same dataset splits; GeoTransolver uses a 20-layer, width-256 transformer with 60,000 surface points.Source: §F.2 · p. 17
  • Held-out validation field-prediction and integrated-force comparisons for the baselines are reported in Table 1 of the main text.Source: §F.2 · p. 18

G.1 DESIGN-VARIABLE RECOVERABILITY

The frozen geometry representation supports accurate linear recovery of design variables, while the same representation is evaluated at held-out flow conditions and transferred to structural prediction with a smaller decoder.

G.1 DESIGN-VARIABLE RECOVERABILITY

  • Mean design-variable probe R2 is 0.989 for SHIFT-SUV, 0.998 for SHIFT-Wing, and 0.998 for SHIFT-Submarine from the frozen 128-dimensional geometry representation.Individual parameter R2 ranges are 0.986–0.995, 0.997–0.999, and 0.996–1.000, respectively.Source: §G.1 · p. 18, Table A.5 · p. 18, Figure A.4 · p. 19

G.2 CONTINUOUS OPERATING-CONDITION GENERALIZATION

  • On SHIFT-Wing, pressure prediction remains above R2 = 0.990 across Mach 0.50–0.90, including held-out Mach 0.7750 and 0.8125 with R2 = 0.9922 and R2 = 0.9944.Ten Mach states are used during training; the two stated Mach numbers are held out entirely.Source: §G.2 · p. 19

G.3 CROSS-PHYSICS DECODER TRANSFER

  • For AutoHood 3D structural displacement transfer, freezing the pretrained aerodynamic encoder leaves 0.56 M trainable decoder parameters versus 2.30 M when trained from scratch, a 4.1× reduction.Source: §G.3 · p. 19

H DIFFERENTIABLE DESIGN OPTIMIZATION

Differentiable design optimization propagates objectives through the learned geometry representation and physics decoder to design variables. The evaluation reports strong alignment between optimized objectives and latent search directions, while runtime estimates and the broader evaluation remain bounded by stated scope and measurement caveats.

H DIFFERENTIABLE DESIGN OPTIMIZATION

  • Gradients flow from the predicted-field objective through the physics decoder and geometry representation back to the design variables.The geometry generator maps design variables to geometry, and the objective is computed from the predicted physical field.Source: H DIFFERENTIABLE DESIGN OPTIMIZATION · pp. 19–20
  • Objective correlations were approximately R2 = 0.99, 0.99, and 0.98 for SHIFT-Wing, SHIFT-SUV, and SHIFT-Submarine optimization trajectories, respectively.Design-variable bounds and a k-nearest-neighbor trust-region constraint keep optimization within the learned design space; resulting candidates are validated against high-fidelity CFD in Table 6.Source: H DIFFERENTIABLE DESIGN OPTIMIZATION · p. 20

I COMPUTATIONAL HARDWARE AND RUNTIME REQUIREMENTS

J LIMITATIONS

  • Evaluation is limited to a small set of parameterized engineering datasets, with cross-physics transfer shown in only one CFD-to-structural setting.The optimization experiments use differentiable surrogates and predefined objectives within the evaluated design spaces; broader benchmarks and constrained real-world optimization remain future evaluation directions.Source: J LIMITATIONS · p. 21

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