# Multi-task Modeling for Engineering Applications with Sparse Data

arXiv: https://arxiv.org/abs/2601.05910 · HTML: https://mlsanity.com/paper/2601.05910/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 9 Jan 2026.

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

- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Sampling](https://mlsanity.com/paper/2310.03298/) (2023)
- [Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains](https://mlsanity.com/paper/2202.12636/) (2022)

## Abstract (arXiv)

Modern engineering and scientific workflows often require simultaneous predictions across related tasks and fidelity levels, where high-fidelity data is scarce and expensive, while low-fidelity data is more abundant. This paper introduces an Multi-Task Gaussian Processes (MTGP) framework tailored for engineering systems characterized by multi-source, multi-fidelity data, addressing challenges of data sparsity and varying task correlations. The proposed framework leverages inter-task relationships across outputs and fidelity levels to improve predictive performance and reduce computational costs. The framework is validated across three representative scenarios: Forrester function benchmark, 3D ellipsoidal void modeling, and friction-stir welding. By quantifying and leveraging inter-task relationships, the proposed MTGP framework offers a robust and scalable solution for predictive modeling in domains with significant computational and experimental costs, supporting informed decision-making and efficient resource utilization.