# Two-Stage Surrogate Modeling for Data-Driven Design Optimization with Application to Composite Microstructure Generation

arXiv: https://arxiv.org/abs/2401.02008 · HTML: https://mlsanity.com/paper/2401.02008/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 82 references that are in the map.
- First posted on arXiv 4 Jan 2024.

## Builds on (most cited first, 21 of 21)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning](https://mlsanity.com/paper/2007.04074/) (2020)
- [Challenges in Deploying Machine Learning: a Survey of Case Studies](https://mlsanity.com/paper/2011.09926/) (2020)
- [Hyperparameter Optimization: Foundations, Algorithms, Best Practices and Open Challenges](https://mlsanity.com/paper/2107.05847/) (2021)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [Physics-informed neural networks for inverse problems in supersonic flows](https://mlsanity.com/paper/2202.11821/) (2022)
- [Cross-validation: what does it estimate and how well does it do it?](https://mlsanity.com/paper/2104.00673/) (2021)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Solving inverse problems using conditional invertible neural networks](https://mlsanity.com/paper/2007.15849/) (2020)
- [Polymer Informatics: Current Status and Critical Next Steps](https://mlsanity.com/paper/2011.00508/) (2020)
- [Bayesian operator inference for data-driven reduced-order modeling](https://mlsanity.com/paper/2204.10829/) (2022)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Structural engineering from an inverse problems perspective](https://mlsanity.com/paper/2106.15177/) (2021)
- [Efficient Surrogate Models for Materials Science Simulations: Machine Learning-based Prediction of Microstructure Properties](https://mlsanity.com/paper/2309.00305/) (2023)
- [Kernel Ridge Regression Using Importance Sampling with Application to Seismic Response Prediction](https://mlsanity.com/paper/2009.09136/) (2020)
- [A Randomized Approach to Efficient Kernel Clustering](https://mlsanity.com/paper/1608.07597/) (2016)

## Built on by (most cited first, 2 of 2)

- [Probabilistic Neural Networks (PNNs) with t-Distributed Outputs: Adaptive Prediction Intervals Beyond Gaussian Assumptions](https://mlsanity.com/paper/2503.12354/) (2025)
- [Surrogate-Assisted Framework for SI-Compliant Interconnect Design Optimization Using the Earth Mover's Distance](https://mlsanity.com/paper/2606.15234/) (2026)

## Abstract (arXiv)

This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the "learner" identifies a limited set of candidates within the input design space whose predicted outputs closely align with desired outcomes. Subsequently, in the second stage, a separate surrogate model, functioning as an "evaluator," is employed to assess the reduced candidate space generated in the first stage. This evaluation process eliminates inaccurate and uncertain solutions, guided by a user-defined coverage level. The framework's distinctive contribution is the integration of conformal inference, providing a versatile and efficient approach that can be widely applicable. To demonstrate the effectiveness of the proposed framework compared to conventional single-stage inverse problems, we conduct several benchmark tests and investigate an engineering application focused on the micromechanical modeling of fiber-reinforced composites. The results affirm the superiority of our proposed framework, as it consistently produces more reliable solutions. Therefore, the introduced framework offers a unique perspective on fostering interactions between machine learning-based surrogate models in real-world applications.