Generative Design of a Gas Turbine Combustor Using Invertible Neural Networks

Abstract: The need to burn 100% H2 in high efficient gas turbines featuring low NOx combustion in premix mode require the complete redesign of the combustion system to ensure stable operation without any flashback. Since all engine frames featuring a power range from 4 MW up to 600 MW are affected, a huge design effort is expected. To reduce this effort, especially to transfer knowledge between the different engine classes, generative design methods using latest AI technology will provide promising potential. In this work, this challenge is approached utilizing the current advances in generative artificial intelligence. We train an Invertible Neural Network (INN) on an expandable database of geometrically parameterized combustor designs with simulated performance labels. Utilizing the INN in its inverse direction, multiple design proposals are generated which fulfill specified performance labels.

• The paper introduces invertible neural networks (INNs) that transform performance targets into multiple feasible combustor designs with high precision.
• It combines detailed CFD simulations and surrogate models to robustly map design parameters to performance labels across a diverse dataset.
• Results demonstrate reduced numerical errors and enhanced design diversity, outperforming Gaussian Process baselines for scalable exploration.

Generative Design of Gas Turbine Combustors via Invertible Neural Networks

Motivation and Background

The transition to zero carbon emissions in large-scale power generation necessitates significant advances in gas turbine combustor design. Specifically, the shift to fuel-flexible turbines capable of burning 100% H$_2$ in premix mode introduces pronounced challenges in ensuring stable combustion, low NO$_x$ emissions, and avoiding flashback. Conventional iterative design approaches, which rely heavily on parametric sweeps and computational fluid dynamics (CFD) simulations, are insufficiently scalable for the extensive design space, and often produce only a single viable design rather than exposing a range of alternatives. Legacy surrogate models, though expediting performance estimation, retain the forward-only paradigm and do not allow for prompt inversion from performance targets to feasible design parameters.

Generative AI, specifically invertible neural networks (INNs), are positioned to fundamentally alter this workflow. INNs, built on normalizing flows and affine coupling architectures, allow accurate modeling of conditional distributions of parameter vectors given performance targets. Consequently, the inverse design problem is re-cast as density estimation and generative inference, allowing rapid generation of multiple alternative geometries that comply with specified performance criteria. This paradigm enables the transfer of design knowledge across different engine classes and facilitates the inclusion of manufacturing and economic criteria by presenting a catalogue of feasible solutions.

Figure 1: Generative design workflow, mapping requirements to multiple geometry alternatives via INN.

Dataset Generation and Physical Modeling

The foundational dataset comprises parametrized combustor geometries, each defined by six independent parameters: ratio of free area at vortex generators ($R_A$), number of fuel injection holes ($N_H$), premixing tube diameter ($D_M$), ratio of lance to tube diameter ($R_D$), length-to-diameter ratio of the premixing tube ($R_L$), and combustor plenum length ($L_P$).

CFD and acoustic network simulation tools (Siemens STAR-CCM+, GeneAC) are employed to obtain three performance labels for each design: pressure loss ($\Delta p_{t,\text{rel}}$), unmixedness ($U_M$), and thermoacoustic growth rate ($_x$0). These labels are critical for assessing efficiency, emissions, and stability.

The CFD mesh features polyhedral elements and targeted refinement in regions of interest, with steady-state RANS and FGM combustion models applied to capture relevant phenomena. Thermoacoustic analysis via the $_x$1-$_x$2 model provides direct mapping from geometry to stability metrics.

Figure 2: Overview of parameterized combustor geometry, illustrating roles of $_x$3 in workflow.

Figure 3: Velocity $_x$4, progress variable $_x$5, and mixing quality visualizations for an exemplary flow field.

Figure 4: Quarter wave mode (86 Hz) profile from acoustic simulation.

Figure 5: Three quarter wave mode (204 Hz) profile from acoustic simulation.

1295 unique data points are generated via Latin Hypercube sampling, ensuring uniform exploration of the design space. Parameter-label relationships reveal strong nonlinear dependencies, particularly between $_x$6, $_x$7, and both pressure loss and unmixedness, underpinning the need for flexible modeling architecture.

Figure 6: Scatter plot showing design parameter-label relationships and stability boundaries across dataset.

Invertible Neural Networks: Methodology

The inverse design problem is characterized by information loss—multiple distinct parameter vectors can yield identical performance labels, precluding direct inversion. INNs address this by learning a bijective mapping from the high-dimensional parameter space to the combined space of labels and latent variables ($_x$8), which encode the hidden degrees of freedom.

Training of INNs proceeds in both forward (parameter to label) and backward (label plus latent to parameter) directions. Forward losses are enforced via MSE (for labels) and MMD (for latent distributions), while backward losses are exclusively MMD-based. The affine coupling block architecture ensures computational tractability and invertibility, with alternating blocks and coordinate permutations enhancing variable interdependence.

Figure 7: INN motivation—latent variable $_x$9 resolves multiplicity in inverse mapping problem.

Figure 8: INN training in both directions, detailing losses and flow of information.

Figure 9: Operations within a coupling block, elucidating invertible computation in forward/backward passes.

Universal approximation guarantees for INNs ensure feasibility in capturing the requisite mapping [ardizzone2018analyzing, ishikawa2023universal].

Implementation, Tuning, and Data Augmentation

The INN is constructed with ten coupling blocks, each with subfunctions as three-layer feedforward networks (115 neurons, ReLU activations). Training leverages the Hyperband algorithm for hyperparameter search, SMAC3 for Bayesian optimization, and Adam optimizer with tuned loss weightings.

A crucial aspect is the use of surrogate models—deep networks trained to emulate CFD and acoustic simulation outputs—for rapid performance prediction during hyperparameter tuning and dataset augmentation. Augmentation extends the dataset to up to 200,000 points, markedly enhancing generative diversity and precision.

Figure 10: Error trends ($R_A$0) as a function of augmented dataset size, demonstrating performance improvements.

INN and surrogate model training is highly efficient on modern GPUs, while CFD simulation is the primary bottleneck in original data generation.

Numerical Results and Analysis

Design targets are specified in a three-dimensional grid across $R_A$1, $R_A$2 and $R_A$3; for each, 5000 candidate parameter vectors are generated by the INN. Filtering ensures consistency within dataset bounds, followed by selection of top-performing and maximally diverse design alternatives.

Figure 11: Distributions of generated parameter vectors $R_A$4 across different target values.

Figure 12: Distributions of generated performance labels $R_A$5 for corresponding targets, demonstrating alignment.

Across the 27 target combinations, the INN achieves high numerical precision—mean errors for $R_A$6 are consistently $R_A$7, $R_A$8 achieves deviations within $R_A$9, and $N_H$0 values group tightly around targets, with uncertainly maximized at the stability boundary ($N_H$1). The performance labels, especially $N_H$2, exhibit strong correlation with specific design parameters, reflecting physical intuition.

The INN generative workflow dominates the Gaussian Process (GP) baseline in both accuracy and diversity, with relative error reductions exceeding 90% for several target values. INN inference is effectively instantaneous, enabling interactive design exploration.

Implications and Future Directions

Practically, this research establishes a scalable, invertible workflow for combustor design addressing multiple performance criteria. The method yields diverse solution sets, enabling post-processing for manufacturability and cost considerations. Expansion to higher dimensional parameter spaces and additional labels, including flashback propensity, is immediate given the scalable architecture and data regime.

Theoretically, the successful application of INNs to physical inverse design reinforces their suitability for problems characterized by dimensionality mismatch and hidden degrees of freedom, with universal approximation and tractable density estimation providing strong technical guarantees.

Anticipated developments include integration of experimental data, active learning for dataset expansion, and further application to free-form design spaces. This approach provides a robust foundation for AI-driven generative engineering in energy systems.

Conclusion

Invertible neural networks offer an efficient, accurate, and diverse generative design workflow for gas turbine combustors, supporting fuel flexibility and emission targets in modern power generation (2604.24322). The methodology reliably maps performance criteria to parameter vectors, outstripping conventional inverse modeling approaches. Surrogate-augmented data and scalable architectures extend applicability, promising future developments in active learning and experimental integration.