Jiacheng Zhao

Topic

Accelerating PolyFEM Triangular Mesh Impact Simulation with Machine Learning Surrogates

Department of Computer Science

Date & location

• Wednesday, August 12, 2026

• 11:00 A.M.

• Virtual Defence

Reviewers

Supervisory Committee

• Dr. Teseo Schneider, Department of Computer Science, University of Victoria (Supervisor)

• Dr. George Tzanetakis, Department of Computer Science, UVic (Member) 

External Examiner

• Dr. Bosco Yu, Department of Mechanical Engineering, University of Victoria 

Chair of Oral Examination

• Dr. Rogerio de Sousa, Department of Physics and Astronomy, UVic 

Abstract

Nonlinear transient finite element method (FEM) simulation of impact on trian gular meshes is computationally expensive. In PolyFEM,22 a single forward solve takes on the order of minutes per design, and a combined forward and adjoint pass takes longer. This makes parameter sweeps and gradient based optimization, which each issue thousands to millions of evaluations, impractical to run on PolyFEM di rectly. This thesis develops two machine learning surrogates over the design parameters (θ,h,E), namely mesh apex angle, wall thickness, and Young’s modulus. The surrogates replace each FEM call with sub-millisecond inference. 

The forward surrogate predicts the peak Von Mises stress on the impacting block. XGBoost with twenty-two features informed by physics and a log(1+y) target transform achieves R2 = 0.97 and Acc@10% = 74.1% on a test set that the model never saw during training. The gradient surrogate predicts the three adjoint sensitivities dL/dE, dL/dh, dL/dθ by decomposing each target into its sign and the logarithm of its magnitude, which handles gradients spanning six to nine orders of magnitude. The decomposition works regardless of model family. XGBoost and a multihead neu ral network agree within a few percentage points across the three components, with Acc@20% ranging from about 47% in the hardest regime past the bifurcation to about 75% on the smoother gradients. 

Both surrogates show the same pattern. Difficulty tracks the underlying physics, and phase transitions impose a noise floor that no architecture can overcome. The thesis pairs the surrogates with a deployment analysis that matches each accuracy regime to the workflows it supports, so that surrogates and PolyFEM are used to gether rather than as substitute.¹

 ¹Code, trained checkpoints, and reproduction instructions are available at https://github.com/ realzjc/uvic-thesis-zjc-code