BladeSDF : Unconditional and Conditional Generative Modeling of Representative Blade Geometries Using Signed Distance Functions

Generative AI has emerged as a transformative paradigm in engineering design, enabling automated synthesis and reconstruction of complex 3D geometries while preserving feasibility and performance relevance. This paper introduces a domain-specific implicit generative framework for turbine blade geometry using DeepSDF, addressing critical gaps in performance-aware modeling and manufacturable design generation. The proposed method leverages a continuous signed distance function (SDF) representation to reconstruct and generate smooth, watertight geometries with quantified accuracy. It establishes an interpretable, near-Gaussian latent space that aligns with blade-relevant parameters, such as taper and chord ratios, enabling controlled exploration and unconditional synthesis through interpolation and Gaussian sampling. In addition, a compact neural network maps engineering descriptors, such as maximum directional strains, to latent codes, facilitating the generation of performance-informed geometry. The framework achieves high reconstruction fidelity, with surface distance errors concentrated within $1\%$ of the maximum blade dimension, and demonstrates robust generalization to unseen designs. By integrating constraints, objectives, and performance metrics, this approach advances beyond traditional 2D-guided or unconstrained 3D pipelines, offering a practical and interpretable solution for data-driven turbine blade modeling and concept generation.

Application of probabilistic modeling and automated machine learning framework for high-dimensional stress field

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer models makes it computationally intensive to query them hundreds of times for optimization and one usually relies on a simplified model albeit at the cost of losing predictive accuracy and precision. Towards this, data-driven surrogate modeling methods have shown a lot of promise in emulating the behavior of the expensive computer models. However, a major bottleneck in such methods is the inability to deal with high input dimensionality and the need for relatively large datasets. With such problems, the input and output quantity of interest are tensors of high dimensionality. Commonly used surrogate modeling methods for such problems, suffer from requirements like high number of computational evaluations that precludes one from performing other numerical tasks like uncertainty quantification and statistical analysis. In this work, we propose an end-to-end approach that maps a high-dimensional image like input to an output of high dimensionality or its key statistics. Our approach uses two main framework that perform three steps: a) reduce the input and output from a high-dimensional space to a reduced or low-dimensional space, b) model the input-output relationship in the low-dimensional space, and c) enable the incorporation of domain-specific physical constraints as masks. In order to accomplish the task of reducing input dimensionality we leverage principal component analysis, that is coupled with two surrogate modeling methods namely: a) Bayesian hybrid modeling, and b) DeepHyper's deep neural networks. We demonstrate the applicability of the approach on a problem of a linear elastic stress field data.