Single-instance, multi-target learning of 3D architectural gridshells for material reuse and circular economy Andrea Favilli1,2,* , Francesco Laccone1 , Paolo Cignoni1 , Luigi Malomo1 and Daniela Giorgi1 1 Institute of Information Science and Technologies "A. Faedo" (ISTI), National Research Council of Italy (CNR), via G. Moruzzi 1, Pisa, 56124, Italy 2 University of Pisa, Lungarno Pacinotti 43, Pisa, 56126, Italy Abstract We propose a learning-based method for the assisted design of 3D architectural free-form gridshells which reuse elements from dismantled, old buildings. Given a gridshell design as input, the output is a learned gridshell whose shape has been modified to reuse as many stock elements as possible, while preserving the design intent and optimizing for statics performance. The main idea is to perform multi-target shape optimization as a single-instance machine learning task, featuring differentiable losses that account for both structural and stock constraints. Since our approach enables the reuse of existing elements for new designs, it reduces the need for sourcing new materials and for disposing waste. Therefore, it contributes to switch to a circular economy and alleviate the environmental impact of the construction sector. Keywords 3D Learning, Multi-agent Learning, Architectural Geometry, Assisted 3D Design, Sustainable Buildings, Environmental Impact, Circular Economy 1. Introduction disassembled structures, where the stock of available ma- terial includes individual structural elements (beams) of The construction sector is responsible for over 35% of specified length and cross section. 3D gridshell structures the total waste generation in Europe, and for a large frac- are discrete networks of straight bars (the beams) con- tion of the overall energy consumption and greenhouse nected by joints at the nodes [2]. Gridshells are ganing gas emissions [1]. Indeed, new constructions require momentum in free-form surface design, as they can cover large volumes of material, and demolitions produce large large spaces while keeping the amount of material rela- amounts of waste. These figures are expected to rise in tively small. Figure 1 shows three examples of gridshells the next decades, due to the growing of the population located in London, Warsaw and Singapore. and its demands. Starting from a initial design, we propose a multi- A possible solution to reduce the environmental and target, learning-based method that aligns the gridshell societal impact of the construction industry is to recycle beams to the stock of available beams, while at the same or reuse construction materials. Recycling means repro- time improving the statics performance of the whole cessing waste to generate new products, while reusing structure. Differently from existing techniques, which means recirculating existing elements and using them are either based on heuristics for solving assignment for new constructions. In particular, increasing reuse in problems or on mixed integer optimization, we leverage the construction sector has the potential to save material on recent advances in 3D deep learning for architectural and energy, as it avoids sourcing new materials, and to geometry [3], and cast the problem as a single-instance reduce waste at the same time. learning task. The input is the original design of a grid- One of the main barriers that hinder reuse in con- shell, and the output is a gridshell whose elements’ shape struction is that the design of structures from stocks of has been modified to reuse as many stock elements as pos- reclaimed elements is totally different from traditional de- sible, while preserving the design intent and optimizing sign. Since the designed structure has to conform to the for statics performance. available elements and their characteristics (e.g., length), The pipeline works in two steps (Figure 2). The first one has to rethink the whole design process. step improves the structural compliance of the gridshell, In this paper, we propose a method for the assisted by means of a neural network featuring a loss that takes design of 3D architectural free-form gridshells from fully- stress into account; the second step assigns stock beams Ital-IA 2024: 4th National Conference on Artificial Intelligence, orga- to gridshell beams, with the assignment problem modeled nized by CINI, May 29-30, 2024, Naples, Italy using soft constraints included in a differentiable loss. * Corresponding author. For the first time, we extend stock-constrained struc- $ andrea.favilli@isti.cnr.it (A. Favilli) tural optimization to 3D gridshells, which are more com-  0009-0004-9342-7106 (A. Favilli); 0000-0002-3787-7215 plex structures than those addressed by the state of the (F. Laccone); 0000-0002-2686-8567 (P. Cignoni); 0000-0001-7892-894X (L. Malomo); 0000-0002-6752-6918 (D. Giorgi) art, mostly 2D structures made of trusses. Also, for the © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License first time we propose a learning strategy to combine Attribution 4.0 International (CC BY 4.0). CEUR ceur-ws.org Workshop ISSN 1613-0073 Proceedings Figure 1: Examples 3D gridshells: from left to right, the Queen Elizabeth II Great Court at the Britsh Museum in London, Złote Tarasy in Warsaw, Changi Airport Jewel in Singapore. material reuse and environmental impact minimization of triangular beam nets approximating freeform surfaces. with the optimization of structural performance, manda- While beams experience axial forces and moments, trans- tory to ensure stiffness, equilibrium, and durability of 3D verse shear and bending, trusses are only subject to ax- architectural structures. ial forces. Moreover, most existing layout optimization We describe a real-world case study, in which the size methods seek an optimal shape configuration for the recy- and capacity of the beam stock are defined from an exist- cled stock from scratch. Instead, we improve an existing ing building to dismantle in Tuscany, Italy. We demon- design shape provided as input. strate how our single-instance learning method enables Finally, while the works mentioned above assign the the reuse of a large fraction of the available material for available elements through constrained optimization, we the design of statics-aware 3D freeform gridshells. Our define soft constraints to frame the reuse problem into a approach can contribute to switch to a circular economy, single-instance machine learning task. We leverage on and to alleviate the environmental impact of architectural[3], in which a geometric deep learning model performs buildings. statics-driven optimization while preserving the origi- nal shape design of the input grid shell. In the present paper, we incorporate a vertex correction optimizer to 2. Related work ensure compatibility of elements with the available stock, and blend the learning model and the optimizer in a In response to the pressing environmental and economic multi-target architecture. In this way, we simultaneously demands, reuse strategies are being prioritized in archi- achieve two objectives: minimizing static compliance tecture and in the construction industry. The initiatives by reducing the strain energy, and enabling the reuse encompass a variety of structures and constitutive el- of elements through a soft-constrained beam matching ements (e.g., trusses, beams, and panels), and employ procedure. In contrast, in existing works the only target different optimization paradigms to minimize for exam- is the reuse of elements, while the static performance is ple material cost and carbon emissions. considered only to guarantee the structure feasibility by In particular, there has been considerable attention including hard constraints [4]. to the design of new structures starting from stocks of elements from old structures. Brütting et al. [4] perform layout optimization of bidimensional structures starting 3. Methods and results from recycled stocks of trusses. The layout optimiza- tion starts from a template structure and selects truss Our aim is to reuse building elements from old structures elements to determine the final topology. Elements from to build new 3D grdshells, which conform to a given de- the batch are matched to their position in the assembled sign and are also optimal in terms of statics performance. structure through mixed-integer optimization. Similarly, Given a 3D gridshell as input with the sought shape, we Van Marcke et al. [5] explore truss reuse by organizing learn a new, improved gridshell, in which the shape of recycled trusses to form planar frameworks, rather than the single elements is optimized to conform to the stock undertaking layout optimization. Expanding beyond the of available ones, while the overall shape is optimized to flat scenario, Brütting et al. [6] provide an algorithmic improve statics performance. solution to build 3D frames made of hexahedral cells of The idea is to perform multi-target shape optimization recycled trusses. on gridshells as a single-instance machine learning task. Unlike the aforementioned studies, which optimize Classical multi-target methods usually incorporate all op- truss structures, our work targets gridshells consisting timization targets into a single loss function, expressed Figure 2: The pipeline of our method. Our single-instance, multi-target learning model involves two agents (blue boxes): a geometric deep learning model (Agent1) and a vertex correction displacer (Agent2). The learning model consumes an input mesh and produces an intermediate shape to be fed to the vertex displacer and to minimize mean strain energy. The displacer optimizes for the assignment of stock beams to gridshell elements, and preserves fairness with respect to the intermediate result (through area variance and Chamfer distance). The agents are driven by different losses (light blue boxes) and collaborate to achieve both material reuse and good statics performance. as a weighted sum of components. However, assign- strain energy of the shape corrected by Agent2; in turn, ing weights to components can be tricky, especially if Agent2 displaces vertices to ensure the alignment with different scales are involved, and if the targets are con- the recycled stock, taking care not to increase the Cham- flicting. Therefore, instead of using a heterogeneous loss, fer distance from the shape produced by Agent1. This we involve the interaction of two agents: a geometric ensures smooth convergence and, as a byproduct, the deep learning model (Agent1 in Figure 2) and a vertex final, optimized design is also consistent with the input displacer (Agent2 in Figure 2). Each agent is driven by shape in terms of geometric features. distinct optimization targets (statics for Agent1, reuse of To test our technique, we identified a disposing indus- elements for Agent2) and corresponding loss functions. trial building located in Pisa, Tuscany, whose roof bays Given a triangle mesh representing the initial grid shell are made of truss-like structural units adequate to be structure, the learning model (Agent1) operates on the reused as beams for a new gridshell. We examined the mesh geometry to optimize the mean strain energy of the original project of the donor building and extracted a het- structure. then, the optimizer (Agent2) corrects the new, erogeneous stock of units whose lengths span from 0.75 learned vertex positions to align the beam lengths with to over 6 meters, with 288 elements available for each of the ones available in the stock. We take into account both the 9 available lengths. Figure 3 shows an example 3D beam lengths and stock capacity. Indeed, the corrections gridshell that could be constructed using the stock of ele- ensure that the number of beams matched to a particular ments from the disposed building. Figure 3(a, left) shows length does not exceed their capacity in the stock. the input design and the optimized output; (a, middle) the Our process is framed as a single-instance learning color-coded expected structure deformation in meters; task, where both agents iteratively learn from the input and (a, right) the edge strain energy of the structure under gridshell structure. Iterations consist of interleaved steps service load; red (resp. blue) means higher (resp. lower) of the two agents. Each agent has its own loss (light values. It can be seen that the expected deformation of blue boxes in Figure 2), and collaboration between the the optimized structure is significantly lower, implying agents is achieved through mutual agreement: the learn- better statics performance for the building; analogously, ing model (Agent1) adjusts its weights to enhance the the strain energy on edges is significantly reduced. deformation (m) strain energy (kJ) 3.0 1.4 1.2 2.5 1.0 2.0 0.8 1.5 0.6 input 1.0 0.4 0.2 0.5 0.0 0.0 3.0 1.4 1.2 2.5 1.0 2.0 0.8 1.5 output 0.6 1.0 0.4 0.2 0.5 0.0 0.0 (a) structural target 1000 950 800 Number of elements 600 400 Stock capacity 259 287 287 200 0 0 0 3 3 2 0 0.7 ed 5m m 5m m 5m m 5m 4m m tch 0.8 1.1 1.4 6.4 1.0 1.3 2.9 ma Un Stock length (b) reuse target Figure 3: Results of our method on a sample freeform shape. (a) Left: the shape provided as input and the multi-target optimized output. Middle: the deformation of the structural nodes under the action of Service Load. Right: the strain energy for each beam. (b) Left: a bar diagram showing the assignment of beams to the input stock. Right: the beam assignment shown through colored edges on the output shape. Figure 3(b, left) reports a bar chart with the assignment other designs could have been produced. This is different of stock elements, and (b, right) the output gridshell with from what is enabled by existing techniques, which only the location of reused elements (color-coded according look for compatible designs, given the available stock. to their lengths). A large fraction of stock elements has Therefore, our technique leaves to the architect complete been reused, apart from the shortest and longest ones design freedom, while taking care of structural perfor- (note that longer elements can be cut and then reused, mance and environmental impact. yet cutting comes with a cost). Also, the shape and style features of the original design have been fully preserved. It is important to underline that our method enables 4. Conclusions the reuse of stock of elements for any input gridshell The reuse of structural elements for the design and fabri- design: Figure 3 only shows an example, whereas many cation of new architectural structures has the potential to greatly reduce the environmental impact of the construc- tion industry. Increasing reuse comes with the challenge of formulating new design paradigms, which take into ac- count the characteristics of the available material without affecting design freedom. At the same time, such design paradigms should take into account statics performance. In this paper, we define a learning-based technique that addresses all three points above for the design of 3D grid- shells, as demonstrated by a real-world case study on the reuse of elements from an existing building. Acknowledgments This work was supported by the NextGenerationEU pro- gramme under the funding schemes PNRR-PE-AI scheme (M4C2, investment 1.3, line on AI) FAIR “Future Artificial Intelligence Research", grant id PE00000013. References [1] European Commission, Buildings and Con- struction, Accessed Apr. 2024. URL: https: //single-market-economy.ec.europa.eu/industry/ sustainability/buildings-and-construction_en. [2] S. Adriaenssens, P. Block, D. Veenendaal, C. Williams, Shell structures for architecture: form finding and optimization, Routledge, 2014. [3] A. Favilli, F. Laccone, P. Cignoni, L. Malomo, D. Giorgi, Geometric deep learning for statics- aware grid shells, Computers & Structures 292 (2024) 107238. URL: https://www.sciencedirect. com/science/article/pii/S0045794923002687. doi:10. 1016/j.compstruc.2023.107238. [4] J. Brütting, J. Desruelle, G. Senatore, C. Fivet, De- sign of truss structures through reuse, Structures 18 (2019) 128–137. 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