Learning Discrete Equilibrium
Trans-topological Inverse Pattern and Force Design Using Machine Learning & Automatic Differentiation
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Date
2023
Publication Type
Doctoral Thesis
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yes
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Abstract
This thesis uses Machine Learning (ML) and Automatic Differentiation (AD) to support the inverse design exploration of reticulated equilibrium shell structures (RESS) across trans-topological design spaces. Such structures are constrained configurations of three design aspects, namely geometry, force and pattern (sometimes referred to as connectivity, layout, or topology). These design aspects prescribe one another’s feasible design space that may be explored: their design exploration, especially under additional performance constraints, is a task that can be challenging even for expert structural designers. The presented work responds to these challenges, addressing in particular the paucity of performance-driven methods for generating and modifying the pattern designs of RESS, and outstanding limitations related to xy-constrained form-finding by Thrust Network Analysis (TNA).
Structured around five design applications, the doctoral research facilitates the computational design exploration of (A) pattern and (B) force distribution and geometry of reticulated equilibrium shells in two distinct early conceptual design scenarios, namely (I) the ideation of initial designs and, later, (II) their iterative development. Specifically, these applications include (I-A) Best-fit Layoutter, which generates structural patterns according to target geometries; (I-B) Best-fit Form-finder, which predicts the closest equilibrium configurations of force and geometry to fit input patterns to target geometries; (II-A) Layout Editor, which recommends design operations for editing the layouts of RESS designs according to structural criteria often overlooked in existing design methods; and (II-B) Auto Form-finder, which discovers multiple solutions to sparsely conditioned RESS optimisation problems. Finally, the thesis introduces (II-B+) Free Edge Picker to select well-conditioned sub-matrices within larger matrices with graph-based interpretation, assisting in the computation of pseudo-inverses for a critical sub-problem in TNA and thereby improving its numerical stability.
Technically, the research synthesises several advanced ML approaches including Generative Modelling, Reinforcement Learning (RL), Artificial Neural Network, Geometric Deep Learning (GDL), as well as supporting techniques like physics-informed learning, data augmentation, and AD. Notable contributions include (A) CWMeshADFuncMaker, a framework enabling expressive composition and efficient computation of auto-differentiable functions on irregular meshes for both ML and optimization tasks; (B) CWMeshNet, a GDL architecture for direct learning of hierarchical discrete systems like the mesh-like datastructures used to represent RESS systems; and (C) CWMeshDQN, an adaptation of CWMeshNet for RL based on Deep Q-Learning to learn effective goal-conditioned deployment of bespoke decision processes encompassing diverse design operations.
While this research focuses on a particular structural type, the developed approaches can be extended to support the design of other discrete assemblies. In doing so, this thesis aims to contribute knowledge and methods broadly useful for the development of ML applications to support performance-informed structural design exploration—applications offering insights and guidance to structural designers to enrich their capacity to achieve structural design goals.
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published
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Examiner : Block, Philippe
Examiner : Krause, Andreas
Examiner : Van Mele, Tom
Examiner : Brown, Nathan
Examiner : Otani, Robert
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ETH Zurich
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Subject
geometric deep learning; reinforcement learning; Computational design; form-finding; shell structure; inverse design; Automatic differentiation; Submatrix selection problem; Layout optimization; inverse form-finding; pattern generation
Organisational unit
03847 - Block, Philippe / Block, Philippe