LSDO Lab
Methods

Scientific machine learning for MDO

Context
Neural networks can approximate the map from design variables to spatial solution fields for repeated engineering analyses.
Gap
High-fidelity field and derivative data are expensive to generate, especially when many design variables influence the solution.
Research goal
Improve surrogate accuracy and data efficiency by incorporating lower-fidelity physics and compressed sensitivity information into learning.

Selected studies

References
Multifidelity flow learningReduced-Jacobian supervision

Improving learned flow fields with lower-fidelity physics

A graph neural network uses a differentiable panel-method solution to predict RANS flow fields around blended-wing-body aircraft. Trained on 100 CFD cases, the physics-guided model improves volume-field predictions over the data-only network. CFD reanalysis of its optimized geometry finds lift and drag errors below 6%.

Primary paper

Mark Sperry, John T. Hwang. Multifidelity Surrogate Modeling for 3D Aerodynamic Flow Field Prediction Using Graph Neural Networks. AIAA AVIATION 2026 Forum, 2026. Distribution Statement A: Approved for public release; distribution is unlimited. PA# AFRL-2026-2231

DOIPDF
Diagram shows geometry parameterization, panel-method input construction, graph construction, graph-neural-network prediction, field reconstruction, and aerodynamic outputs.
The PG-RANS-GNN workflow pairs geometry and a differentiable panel-method field with a multiscale graph neural network to predict three-dimensional flow fields and aerodynamic coefficients. Fig. 5, Sperry and Hwang, 2026 [1]
CFD pressure fields, physics-guided and data-driven graph-neural-network predictions, and their errors are compared on a randomized aircraft configuration.
On a randomized aircraft configuration, the physics-guided and data-driven GNNs reproduce the major three-dimensional and spanwise pressure features; the error fields identify the remaining local discrepancies with CFD. Fig. 7, Sperry and Hwang, 2026 [1]
CFD pressure, graph-neural-network pressure predictions, and absolute errors are compared at spanwise slices for aircraft optimized with physics-guided and data-driven GNN surrogates.
CFD checks of the geometries optimized with the physics-guided and data-driven GNNs compare their predicted pressure fields and errors over five spanwise slices. Fig. 11, Sperry and Hwang, 2026 [1]

Learning design sensitivities from compressed derivative data

Reduced-Jacobian supervision trains the full state field alongside a compressed derivative representation, making derivative-data collection scale with basis size rather than full input or state dimension. Structural-wing tests with 5–161 inputs show lower displacement and reduced-Jacobian errors than training on state values alone.

Primary paper

Michael Warner, John T. Hwang. Reduced Jacobian Supervision for Data-Efficient Operator Learning in High-Dimensional Design Spaces. AIAA AVIATION 2026 Forum, 2026. Distribution Statement A: Approved for public release; distribution is unlimited. PA# AFRL-2026-2144

DOIPDF
Displacement and reduced-Jacobian prediction error are plotted against a combined training-sample and input-dimension scaling variable.
Fitted error scaling for reduced-Jacobian supervision shows a stronger dimension-related improvement for displacement than for Jacobian prediction. Fig. 7, Warner and Hwang, 2026 [2]

References

  1. Mark Sperry, John T. Hwang. Multifidelity Surrogate Modeling for 3D Aerodynamic Flow Field Prediction Using Graph Neural Networks. AIAA AVIATION 2026 Forum, 2026. Distribution Statement A: Approved for public release; distribution is unlimited. PA# AFRL-2026-2231
    DOIPDF
  2. Michael Warner, John T. Hwang. Reduced Jacobian Supervision for Data-Efficient Operator Learning in High-Dimensional Design Spaces. AIAA AVIATION 2026 Forum, 2026. Distribution Statement A: Approved for public release; distribution is unlimited. PA# AFRL-2026-2144
    DOIPDF
  3. Michael A. P. Warner, John T. Hwang. Structured Reduced-Basis Neural Operators for PDEs on Complex Geometries. ASME IDETC/CIE 2026 · DETC2026-194246, 2026. Distribution Statement A: Approved for public release; distribution is unlimited. PA# AFRL-2026-1143 Manuscript

Research connections

Related to Scientific machine learning for MDO

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