# A Unified Hierarchical Multi-Task Multi-Fidelity Framework for Data-Efficient Surrogate Modeling in Manufacturing

arXiv: https://arxiv.org/abs/2603.09842 · HTML: https://mlsanity.com/paper/2603.09842/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 49 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 5 of 5)

- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [A support vector regression-based multi-fidelity surrogate model](https://mlsanity.com/paper/1906.09439/) (2019)
- [Towards a Digital Twin Framework in Additive Manufacturing: Machine Learning and Bayesian Optimization for Time Series Process Optimization](https://mlsanity.com/paper/2402.17718/) (2024)
- [Accurate and Uncertainty-Aware Multi-Task Prediction of HEA Properties Using Prior-Guided Deep Gaussian Processes](https://mlsanity.com/paper/2506.14828/) (2025)

## Abstract (arXiv)

Surrogate modeling is an essential data-driven technique for quantifying relationships between input variables and system responses in manufacturing and engineering systems. Two major challenges limit its effectiveness: (1) large data requirements for learning complex nonlinear relationships, and (2) heterogeneous data collected from sources with varying fidelity levels. Multi-task learning (MTL) addresses the first challenge by enabling information sharing across related processes, while multi-fidelity modeling addresses the second by accounting for fidelity-dependent uncertainty. However, existing approaches typically address these challenges separately, and no unified framework simultaneously leverages inter-task similarity and fidelity-dependent data characteristics. This paper develops a novel hierarchical multi-task multi-fidelity (H-MT-MF) framework for Gaussian process-based surrogate modeling. The proposed framework decomposes each task's response into a task-specific global trend and a residual local variability component that is jointly learned across tasks using a hierarchical Bayesian formulation. The framework accommodates an arbitrary number of tasks, design points, and fidelity levels while providing predictive uncertainty quantification. We demonstrate the effectiveness of the proposed method using a 1D synthetic example and a real-world engine surface shape prediction case study. Compared to (1) a state-of-the-art MTL model that does not account for fidelity information and (2) a stochastic kriging model that learns tasks independently, the proposed approach improves prediction accuracy by up to 19% and 23%, respectively. The H-MT-MF framework provides a general and extensible solution for surrogate modeling in manufacturing systems characterized by heterogeneous data sources.