Details
| Original language | English |
|---|---|
| Journal | MECCANICA |
| Early online date | 19 Jun 2024 |
| Publication status | E-pub ahead of print - 19 Jun 2024 |
Abstract
The selection of well-conditioned sub-matrices is a critical concern in problems across multiple disciplines, particularly those demanding robust numerical stability. This research introduces an innovative, AI-assisted approach to sub-matrix selection, aimed at enhancing the form-finding of reticulated shell structures under the xy-constrained Force Density Method (also known as Thrust Network Analysis), using independent edge sets. The goal is to select a well-conditioned sub-matrix within a larger matrix with an inherent graph interpretation where each column represents an edge in the corresponding graph. The selection of ill-conditioned edges poses a significant challenge because it can render large segments of the parameter space numerically unstable, leading to numerical sensitivities that may impede design exploration and optimisation. By improving the selection of edges, the research assists in computing a pseudo-inverse for a critical sub-problem in structural form-finding, thereby enhancing numerical stability. Central to the selection strategy is a novel combination of deep reinforcement learning based on Deep Q-Networks and geometric deep learning based on CW Network. The proposed framework, which generalises across a trans-topological design space encompassing patterns of varying sizes and connectivity, offers a robust strategy that effectively identifies better-conditioned independent edges leading to improved optimisation routines with the potential to be extended for sub-matrix selection problems with graph interpretations in other domains.
Keywords
- Form-finding, Geometric deep learning, Matrix conditioning, Reinforcement learning, Shell structures, Sub-matrix selection, Thrust network analysis
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
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In: MECCANICA, 19.06.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Well-conditioned AI-assisted sub-matrix selection for numerically stable constrained form-finding of reticulated shells using geometric deep Q-learning
AU - Tam, K. M.M.
AU - Maia Avelino, R.
AU - Kudenko, D.
AU - Van Mele, T.
AU - Block, P.
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/6/19
Y1 - 2024/6/19
N2 - The selection of well-conditioned sub-matrices is a critical concern in problems across multiple disciplines, particularly those demanding robust numerical stability. This research introduces an innovative, AI-assisted approach to sub-matrix selection, aimed at enhancing the form-finding of reticulated shell structures under the xy-constrained Force Density Method (also known as Thrust Network Analysis), using independent edge sets. The goal is to select a well-conditioned sub-matrix within a larger matrix with an inherent graph interpretation where each column represents an edge in the corresponding graph. The selection of ill-conditioned edges poses a significant challenge because it can render large segments of the parameter space numerically unstable, leading to numerical sensitivities that may impede design exploration and optimisation. By improving the selection of edges, the research assists in computing a pseudo-inverse for a critical sub-problem in structural form-finding, thereby enhancing numerical stability. Central to the selection strategy is a novel combination of deep reinforcement learning based on Deep Q-Networks and geometric deep learning based on CW Network. The proposed framework, which generalises across a trans-topological design space encompassing patterns of varying sizes and connectivity, offers a robust strategy that effectively identifies better-conditioned independent edges leading to improved optimisation routines with the potential to be extended for sub-matrix selection problems with graph interpretations in other domains.
AB - The selection of well-conditioned sub-matrices is a critical concern in problems across multiple disciplines, particularly those demanding robust numerical stability. This research introduces an innovative, AI-assisted approach to sub-matrix selection, aimed at enhancing the form-finding of reticulated shell structures under the xy-constrained Force Density Method (also known as Thrust Network Analysis), using independent edge sets. The goal is to select a well-conditioned sub-matrix within a larger matrix with an inherent graph interpretation where each column represents an edge in the corresponding graph. The selection of ill-conditioned edges poses a significant challenge because it can render large segments of the parameter space numerically unstable, leading to numerical sensitivities that may impede design exploration and optimisation. By improving the selection of edges, the research assists in computing a pseudo-inverse for a critical sub-problem in structural form-finding, thereby enhancing numerical stability. Central to the selection strategy is a novel combination of deep reinforcement learning based on Deep Q-Networks and geometric deep learning based on CW Network. The proposed framework, which generalises across a trans-topological design space encompassing patterns of varying sizes and connectivity, offers a robust strategy that effectively identifies better-conditioned independent edges leading to improved optimisation routines with the potential to be extended for sub-matrix selection problems with graph interpretations in other domains.
KW - Form-finding
KW - Geometric deep learning
KW - Matrix conditioning
KW - Reinforcement learning
KW - Shell structures
KW - Sub-matrix selection
KW - Thrust network analysis
UR - http://www.scopus.com/inward/record.url?scp=85189514920&partnerID=8YFLogxK
U2 - 10.1007/s11012-024-01769-3
DO - 10.1007/s11012-024-01769-3
M3 - Article
AN - SCOPUS:85189514920
JO - MECCANICA
JF - MECCANICA
SN - 0025-6455
ER -