MechE PhD Prospectus Defense: Mohammad (Erfan) Hamdi

TITLE: TOWARD TRUSTWORTHY MACHINE LEARNING IN COMPUTATIONAL MECHANICS: FROM SURROGATE MODELING TO MACHINE REASONING

ABSTRACT: Machine learning has the potential to accelerate computational mechanics, but determining when these models can be trusted remains difficult. Existing evaluations often rely on relatively simple benchmark problems or metrics that can obscure important failures. This dissertation asks how reliability should be evaluated as the application of machine learning moves from approximating physical solutions to reasoning about how those solutions should be constructed. The first part of this dissertation examines neural surrogate models for brittle fracture. We developed PFM-Fracture, a dataset of 6,000 two-dimensional phase-field simulations with randomly generated crack configurations and use it to evaluate several classes of surrogate models and ensemble methods. The results reveal distinct limitations across model classes, including difficulty capturing complex or sharp crack behavior. We also find that performance can vary drastically with neural-network initialization and the choice of evaluation metric. These findings show that conclusions about surrogate-model reliability depend not only on model architecture, but also on how models are trained and evaluated. The second part of this dissertation shifts from prediction to machine reasoning. We developed FEM-Bench, a benchmark for evaluating scientific reasoning in large language models (LLMs) through finite element analysis code generation. FEM-Bench v1 contains 33 graduate-level finite element and matrix structural analysis problems and evaluates whether LLMs can generate correct solution functions and physics-aware unit tests. Even across five attempts, no evaluated model solves every problem. Failure analysis reveals recurring errors due to domain knowledge deficits, lack of algorithmic fidelity, and difficulty with compositional reasoning, with domain knowledge deficits emerging as the main bottleneck. Building on these results, the proposed work will extend FEM-Bench to more challenging and previously unseen mechanics problems and investigate whether agentic systems can improve reliability by generating, executing, and revising finite element code. Together, these studies develop a framework for evaluating machine learning systems across two fundamentally different roles in computational mechanics: predicting physical behavior and constructing computational solutions.

COMMITTEE: ADVISOR/CHAIR Professor Emma Lejeune, ME; Professor Harold Park, ME/MSE; Professor Douglas Holmes, ME/MSE