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UID:event-46@tuemeche.nl
DTSTAMP:20261007T234656Z
DTSTART;TZID=Europe/Amsterdam:20261013T133000
DTEND;TZID=Europe/Amsterdam:20261013T150000
SUMMARY:Equivariant Machine Learning for Simulation of Buckling in Mechan
 ical Metamaterials
DESCRIPTION:Speaker: Fleur Hendriks\nHost: Ondrej Rokos\n\nMechanical met
 amaterials are materials with special properties such as tunable stiffnes
 s and negative Poisson’s ratio\, resulting from their specially designe
 d microstructure. Using structural instabilities like buckling\, these ma
 terials can undergo controlled pattern transformations\, making them suit
 able for applications in soft robotics and tunable sound attenuation. How
 ever\, modelling\, design\, and optimization of such materials are limite
 d by the high computational cost required to simulate these materials usi
 ng conventional methods when deformations are large and there is buckling
 . To address these computational bottlenecks\, this thesis splits into th
 e following main four parts.\n\n1. Accelerated Homogenization via SimEGNN
 \nFirst\, SimEGNN (Similarity-Equivariant Graph Neural Network) is develo
 ped\, which is a neural network that respects fundamental physical symmet
 ries (Euclidean transformations\, periodicity\, and scaling). It predicts
  global quantities like strain energy density\, stress and stiffness as w
 ell as the local deformation field in response to a macroscopic deformati
 on gradient. It provides a high-fidelity alternative to traditional finit
 e-element simulations. Quantitative results demonstrate that this archite
 cture achieves superior data efficiency and provides order-of-magnitude s
 peed-ups on a relevant test system (a microstructure with circular holes 
 arranged in a square grid)\, making it a practical tool for rapid\, itera
 tive design.\n\n2. A Dataset of Wallpaper Group-Based 2D Microstructures\
 nThe development of robust surrogate models requires training data that r
 eflects the full diversity of geometric possibilities. To this end\, this
  thesis introduces a novel dataset of 1\,020 high-quality 2D microstructu
 res spanning all 17 wallpaper groups. These structures are generated via 
 a periodic-graph "skeleton"\, used as a starting point to determine the s
 hape and placement of holes parametrized by Bézier curves\, ensuring con
 nectivity. Each microstructure is simulated across multiple loading traje
 ctories in the hyperelastic\, finite-strain regime including buckling\, p
 roviding a comprehensive resource for studying symmetry-property relation
 ships such as auxeticity and mode multiplicity.\n\n3. Equivariant Flow Ma
 tching for Bifurcation\nA fundamental challenge in modeling buckling meta
 materials is multistability\, where a single input can lead to multiple s
 table states. Because traditional deterministic machine learning models t
 end to average these outcomes into nonphysical predictions\, this thesis 
 introduces a probabilistic\, equivariant flow-matching framework capable 
 of capturing the full distribution of bifurcation outcomes. This framewor
 k is tested on various physical problems that show symmetry-breaking bifu
 rcations. The framework ensures that the learned distributions respect th
 e underlying physical symmetries of the system\, even if individual outco
 mes break those symmetries. The models are trained more efficiently by ut
 ilizing symmetric coupling to find the optimal group-equivalent target fo
 r each sample.\n\n4. An Integrated Pipeline for Deformation Distributions
 \nThe final contribution of this thesis synthesizes the above three eleme
 nts into a unified GNN and Flow-Matching pipeline. This integrated pipeli
 ne takes graph representations of metamaterials as input and generates en
 tire distributions of deformation trajectories under mechanical loading a
 s output. Temporal 1D U-Nets are incorporated to model long-range depende
 ncies within these trajectories. The pipeline offers a powerful\, end-to-
 end tool for predicting the complex\, nonlinear behavior of mechanical me
 tamaterials.\n\nMore info: https://tuenl.sharepoint.com/sites/intranet-me
 chanical-engineering/_layouts/15/Event.aspx?ListGuid=9bfaaae6-070c-4371-8
 10d-a43d7ee02bf2&ItemId=244
LOCATION:Atlas 0.710
URL:https://tuemeche.nl/peoplepages/event.php?id=46
CATEGORIES:PhD Defense
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