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Mechanical Engineering Dissertation Topics

Info: Mechanical Engineering Dissertation Topics
Published: 29th July 2025 in Mechanical Engineering Dissertation Topics

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Dissertation Topic 1:

Development of Active Subspace Methods for Efficient Exploration of High-Dimensional Spaces in Uncertainty Quantification

Background Context

High-dimensional scenarios in uncertainty quantification often led to computational complexity, which can hinder surrogate modelling techniques’ application. There are many different fields of research where active subspace methods can be introduced to reduce dimensionality by allowing the identification of low-dimensional subspaces that account for most of the variance. In this research, the utilisation of active subspaces will be examined to enhance surrogate models, particularly concerning high-dimensional uncertainty quantification problems.

Research Questions

1. How well can multi-fidelity surrogate models be integrated and provide improvements to both accuracy and efficiency in high-dimensional uncertainty quantification problems?
2. What are the challenges and resolutions to integrating high-fidelity and low-fidelity models in the uncertainty quantification process?
3. Compared to single-fidelity surrogate models, what are the differences in performance and costs when using multi-fidelity models?

Potential Implications

  • Enriched surrogate modelling treatments of complex engineering systems with high-dimensional uncertainty.
  • Improved techniques in which to integrate multiple sources of data from varying fidelity models, while minimising both overall costs and accuracy.
  • An increased appreciation of the trade-offs between model fidelity and the available computational resources in uncertainty quantification problems.

    • Suggested Reading

  • Wang, B., Orndorff, N. C., Sperry, M., & Hwang, J. T. (2025). Extension of graph-accelerated non-intrusive polynomial chaos to high-dimensional uncertainty quantification through the active subspace method. Aerospace Science and Technology, 160, 110074.
  • Luneau, P. A. (2025). Conservative surrogate models for optimization with the active subspace method. Engineering Optimization, 1-21.

    • Dissertation Topic 2:

    Physics-Informed Neural Networks (PINNs) for Surrogate Modelling and Uncertainty Quantification in Complex Engineering Systems

    Background Context

    Physics-Informed Neural Networks (PINNs) take advantage of the strengths of machine-learning knowledge with known physical laws to solve problems that would otherwise be computationally expensive with traditional methods. This research project will examine the application of PINNs for surrogate modelling or representation in the context of uncertainty quantification, especially in systems with known physical constraints and high dimensions where we want to include data (and bias) from prior models with known equations. The focus of the research is on obtaining prior physical knowledge in surrogate models to enhance the performance and use of surrogate models in engineering-based problems.

    Research Questions

    1. How can PINNs be applied in uncertainty quantification to improve the accuracy and efficiency of surrogate models?
    2. How does the proposal to incorporate those unknown physical constraints with PINNs to surrogate model allow for generalisation on uncertainty quantification?
    3. In general, how do PINNs learn from both the known and unknown in engineering systems, as compared to traditional machine-learning methods for handling uncertainty in high-dimensional problems?

    Potential Implications

  • Surrogate models that combine physical knowledge and data.
  • Predictive accuracy and efficiency of uncertainty quantification of complex engineering systems.
  • Incorporating relevant physics into models reduces the computational cost while giving reliable uncertainty propagation in high-dimensional problems.

    • Suggested Reading

    • Propp, A. M., & Tartakovsky, D. M. (2025). Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling. Journal of Machine Learning for Modeling and Computing, 6(2).
    • Shi, Y., Wei, P., Feng, K., Feng, D. C., & Beer, M. (2025). A survey on machine learning approaches for uncertainty quantification of engineering systems. Machine Learning for Computational Science and Engineering, 1(1), 11.

    Dissertation Topic 3:

    Dimensionality Reduction Techniques for Improving the Accuracy and Stability of Surrogate Models in High-Dimensional Systems

    Background Context

    One of the main challenges in surrogate modelling, specifically for high-dimensional uncertainty quantification, is the curse of dimensionality. Dimensionality reduction techniques, such as PCA, t-SNE, and autoencoders, are an option for overcoming the curse of dimensionality, allowing us to reduce high-dimensional data into a more manageable format. This research will explore how these dimensionality reduction techniques could be used to facilitate improved accuracy and stability of surrogate models for the purpose of uncertainty quantification.

    Research Questions

    1. What effects do the different dimensionality reduction techniques have on surrogate models for high-dimensional uncertainty quantification?
    2. What are the biases between accuracy and computational burden for different occupations of dimensionality reduction techniques?
    3. What are ways to combine dimensionality reduction techniques with multi-fidelity surrogate models to improve uncertainty quantification?

    Potential Implications

  • Improvements for thinking about high-dimensional data utilising more advanced dimensionality reduction techniques.
  • Improvements in the accuracy and computational efficiency of surrogate modelling in real-world engineering problems.
  • Understanding of the integration of dimensionality reduction techniques, as well as multi-fidelity models for dealing with complex uncertainty quantification problems.

    • Suggested Reading

  • Giovanis, D. G., Taflanidis, A., & Shields, M. D. (2025). Accelerating uncertainty quantification in incremental dynamic analysis using dimension reduction-based surrogate modeling. Bulletin of Earthquake Engineering, 23(1), 391-410.
  • Samaddar, A., Ravi, S. K., Ramachandra, N., Luan, L., Madireddy, S., Bhaduri, A., … & Wang, L. (2025). Data-Efficient Dimensionality Reduction and Surrogate Modeling of High-Dimensional Stress Fields. Journal of Mechanical Design, 147(3), 031701.

    • Dissertation Topic 4:

    Synthetic Data Generation for Sparse Datasets in High-Dimensional Uncertainty Quantification Problems

    Background Context

    Sparse datasets are often a barrier in high-dimensional uncertainty quantification, since sparsity makes it more difficult to construct a good surrogate model. Synthetic data can be created using various methods, with Generative Adversarial Networks (GANs) providing many possibilities and other machine-learning methods also being available for consideration. This study will investigate using synthetic data generation methods to support the limited datasets used to construct surrogate models for uncertainty quantification.

    Research Questions

    1. How can synthetic data generation approaches add value to the abundantly sparse data sets that exist in high-dimensional uncertainty quantification and engineering systems?
    2. What are the possible benefits and drawbacks of generative models like GANs to leverage synthetic data for surrogate modelling?
    3. How will the integration of synthetic data alter the accuracy and stability of uncertainty propagation in the target engineering systems?

    Potential Impact

  • More datasets are available for surrogate modelling of high-dimensional engineering systems.
  • Increased surrogate model performance, through addressing the shortage of data using synthetic data, for uncertainty quantification.
  • Lowered computational costs to enhance better generalisation of models when using complex uncertainty quantification tasks.

    • Suggested Reading

  • Mahadevan, S., & Guo, Y. (2025). Surrogate Modeling and Model Discrepancy Propagation in High-Dimensional Problems. In AIAA SCITECH 2025 Forum (p. 2134).
  • Šturek, D., & Lazarova-Molnar, S. (2025). Surrogate Modeling: Review and Opportunities for Expert Knowledge Integration. Procedia Computer Science, 257, 826-833.

    • Dissertation Topic 5:

    Multi-Fidelity Surrogate Models for Uncertainty Quantification in Complex Engineering Systems: Methods and Applications

    Background context

    Multi-fidelity surrogate models can integrate data of varying fidelity together, allowing us to simultaneously reduce computational cost and maintain accuracy. This research will use multi-fidelity surrogate models to provide a new method for high-dimensional uncertainty quantification for engineering systems by leveraging both higher fidelity simulation data (`high-fidelity’) and the available lower fidelity models (`low-fidelity’) for uncertainty analysis.

    Research Questions

    1. How can multi-fidelity surrogate models/uncertainty quantification be employed and implemented for high-dimensional problems such that accuracy and efficiency are improved?
    2. What hurdles are present and what options exist for overcoming them in the integration of high-fidelity and low-fidelity models for uncertainty quantification?
    3. How does the performance and computational cost of multi-fidelity models compare to using a single-fidelity surrogate model?

    Potential Implications

  • Improved surrogate modelling capability for highly complex engineering systems that are subjected to high-dimensional uncertainty.
  • Improved methodology for the integration of multi-fidelity data to lower computational costs and reduce the increase in error from using lower-fidelity models.
  • Improved understanding of the inherent trade-offs between model fidelity and computational cost in uncertainty quantification tasks.

    • Suggested Readings

  • Kumar, S. (2025). Uncertainty Quantification for Multi-Fidelity Simulations. arXiv preprint arXiv:2503.08408.
  • Xiao, W., Shen, Y., Zhao, J., Lv, L., Chen, J., & Zhao, W. (2025). An Adaptive Multi-Fidelity Surrogate Model for Uncertainty Propagation Analysis. Applied Sciences, 15(6), 3359.

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