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Multi-task Modeling for Engineering Applications with Sparse Data

Yigitcan Comlek, R. Murali Krishnan, Sandipp Krishnan Ravi, Amin Moghaddas, Rafael Giorjao, Michael Eff, Anirban Samaddar, Nesar S. Ramachandra, Sandeep Madireddy, Liping Wang

TL;DR

This work presents a Multi-Task Gaussian Process framework tailored for engineering problems with sparse high-fidelity data and multiple related outputs across fidelity levels. By leveraging coregionalization via Linear Model of Coregionalization and Semiparametric Latent Factor Models, the MTGP captures cross-task dependencies and cross-fidelity structure, enabling data-efficient joint predictions with calibrated uncertainty. The approach is validated on three representative scenarios: Forrester function extensions, 3D ellipsoidal void modeling with elastic and plastic tasks, and friction-stir welding combining experiments with low-cost temperature simulations, with consistent improvements in predictive accuracy and reductions in high-cost data requirements. The results underscore MTGPs as a scalable, robust tool for predictive modeling in data-constrained, multi-output engineering contexts, offering tangible gains in decision quality and resource utilization.

Abstract

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.

Multi-task Modeling for Engineering Applications with Sparse Data

TL;DR

This work presents a Multi-Task Gaussian Process framework tailored for engineering problems with sparse high-fidelity data and multiple related outputs across fidelity levels. By leveraging coregionalization via Linear Model of Coregionalization and Semiparametric Latent Factor Models, the MTGP captures cross-task dependencies and cross-fidelity structure, enabling data-efficient joint predictions with calibrated uncertainty. The approach is validated on three representative scenarios: Forrester function extensions, 3D ellipsoidal void modeling with elastic and plastic tasks, and friction-stir welding combining experiments with low-cost temperature simulations, with consistent improvements in predictive accuracy and reductions in high-cost data requirements. The results underscore MTGPs as a scalable, robust tool for predictive modeling in data-constrained, multi-output engineering contexts, offering tangible gains in decision quality and resource utilization.

Abstract

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.
Paper Structure (16 sections, 15 equations, 5 figures, 6 tables)

This paper contains 16 sections, 15 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Gaussian processes for probabilistic regression
  4. Multi-task learning with vector-valued Gaussian Process
  5. Coregionalization models multi-task modeling
  6. Posterior inference and learning in Coregionalization models
  7. Benchmark - Forrester Function
  8. Ellipsoidal Voids
  9. Elastic Case
  10. Elastic-Plastic Case
  11. Modeling the Friction Stir Welding Process
  12. Data Sources
  13. Modeling Results with MTGP
  14. Conclusions
  15. Acknowledgment
  16. ...and 1 more sections

Figures (5)

  • Figure 1: The multi-task modeling framework for sparse data applications
  • Figure 2: Low (r = 0.33), Medium (r = 0.55), and High (r = 0.89) correlated Forrester functions
  • Figure 3: An example schematic of the ellipsoidal void system
  • Figure 4: Predictive performance (RMSE and % improvement) comparison between MTGP and GP for the elastic and elastic-plastic case studies on von Mises Stress (T1)
  • Figure 5: Friction stir welding modeling framework