[Paper Review] Data efficient surrogate modeling for engineering design: Ensemble-free batch mode deep active learning for regression

Kapoor, Sarthak, Harsh Vardhan+4 more|arXiv (Cornell University)|Nov 16, 2022

Advanced Multi-Objective Optimization Algorithms4 citations

TL;DR

This paper proposes ϵ-HQS, a scalable ensemble-free batch-mode active learning method for deep regression in engineering design, using a student-teacher framework to select informative samples with minimal labeling cost. By training a teacher network to predict failure probabilities based on student model errors, ϵ-HQS achieves higher surrogate model accuracy than baseline methods across CFD, FEA, and propeller design tasks under fixed budget constraints.

ABSTRACT

High fidelity design evaluation processes such as Computational Fluid Dynamics and Finite Element Analysis are often replaced with data driven surrogates to reduce computational cost in engineering design optimization. However, building accurate surrogate models still requires a large number of expensive simulations. To address this challenge, we introduce epsilon HQS, a scalable active learning strategy that leverages a student teacher framework to train deep neural networks efficiently. Unlike Bayesian AL methods, which are computationally demanding with DNNs, epsilon HQS selectively queries informative samples to reduce labeling cost. Applied to CFD, FEA, and propeller design tasks, our method achieves higher accuracy under fixed labeling cost budgets.

Motivation & Objective

• To reduce the high computational cost of generating training data for surrogate models in engineering design by minimizing the number of expensive simulations.
• To address the scalability and efficiency limitations of existing Bayesian active learning methods when applied to deep neural networks.
• To develop a sample-efficient active learning strategy that outperforms random and heuristic-based sampling in high-dimensional design spaces.
• To enable accurate surrogate modeling in complex engineering domains such as CFD, FEA, and propeller design with minimal labeling budget.

Proposed method

• The method employs a student-teacher neural network framework, where the student learns the simulator’s mapping from input design space to output responses.
• The teacher network is trained on a custom 'test report' dataset derived from the student’s predictions, using binary failure labels based on fractional error thresholds (α = 0.05).
• Failure probability is computed as the output of the teacher network, which guides batch sampling toward regions of high prediction uncertainty or error.
• The acquisition function selects the top-k samples with highest predicted failure probability for labeling in each iteration, enabling batch-mode active learning.
• The student and teacher networks are retrained iteratively using newly labeled data until the budget is exhausted.
• The approach uses a dynamic ϵ-scheduling strategy (e.g., logarithmic increase) to balance exploration and exploitation during active learning.

Experimental results

Research questions

• RQ1 Can a teacher-student active learning framework outperform traditional active learning and random sampling in deep regression tasks for engineering design?
• RQ2 How does the proposed ϵ-HQS method improve sample efficiency in high-dimensional design spaces compared to baseline acquisition functions?
• RQ3 To what extent does the ensemble-free, batch-mode design of ϵ-HQS reduce computational overhead while maintaining high surrogate model accuracy?
• RQ4 Does the method scale effectively across diverse engineering domains such as CFD, FEA, and propeller design with varying complexity and dimensionality?

Key findings

• ϵ-HQS achieved 97.62% accuracy in the CFD domain, outperforming the next best method (DBAL-10 at 96.13%) under a total budget of 500 samples.
• In the FEA domain, ϵ-HQS reached 87.56% accuracy, significantly outperforming random sampling (83.76%) and top-B sampling (83.11%).
• For the propeller design task, ϵ-HQS achieved 67.18% accuracy with ϵ = 0.25, surpassing even the greedy ϵ-HQS variant and outperforming all baselines.
• The method demonstrated consistent superiority across all three domains, with performance gains increasing in higher-dimensional problems.
• ϵ-HQS reduced labeling time by hours to days compared to baseline methods, due to its high sample efficiency and minimal reliance on expensive simulations.