Bachelor theses
Neural Network-based Approaches for Solving Minimization Problems in Computational Mechanics
Author
Rafael Galiev
Year
2025
Type
Bachelor thesis
Supervisor
doc. Dr. rer. nat. Ing. Jan Valdman
Reviewers
RNDr. Miroslav Frost, Ph.D.
Department
Summary
This work explores whether compact neural networks can replace the standard
closed-form solution in single-yield elastoplasticity and the minimization-based
formulation used in double-yield models. Feedforward networks were trained
using PyTorch on a static data set with fixed material parameters to emulate
elastoplastic behavior. When evaluated on a test grid with four times as many
points as the training grid, the networks reproduced reference plastic strains
with mean absolute errors below 4 × 10^-3 and delivered 6-10× faster inference
on a commodity GPU (and several-fold gains on CPU). These results suggest
that compact multilayer perceptrons can replace classical constitutive computations with negligible accuracy loss and substantial time savings, offering a practical step toward data-driven models in computational mechanics.