Authors: Sellman, Carl
Source: Figshare (article, 2025-01-01)
Field: Materials Science — Materials Chemistry

Evolvable Penrose Quasicrystal Wave-Energy Farms with AI Surrogate Optimization<b>Author:</b>Carl Sellman (UnAn0n) Defensive Public Disclosure (abridged)<b>Title:</b><br>Evolvable Penrose Quasicrystal Wave-Energy Farms with AI Surrogate Optimization<b>Author:</b><br>Carl Sellman (UnAn0n)<br>Date: 22 November 2025OverviewThis document discloses a class of ocean infrastructure systems and algorithms that use <b>Penrose quasicrystal geometry</b> as the organizing principle for wave-energy extraction, coastal protection, and climate-resilient energy harvesting. The disclosure is intended to serve as prior art to prevent others from obtaining patent rights on the core ideas described below.1. Penrose-Based Macro Layout of Floating Wave FarmsThe proposed system deploys floating modules (e.g. wave energy converters, pontoons, or multi-function platforms) at the <b>vertices of a Penrose tiling</b>, specifically a Penrose rhomb tiling generated by a pentagrid construction.A finite Penrose patch is generated by:Defining <b>five families of parallel lines</b> in the plane, each with an orientation and a scalar offset parameter γₖ (k = 0…4).Computing intersection points of these lines within a bounded region controlled by a scalar <b>grid radius parameter R_grid</b>.The intersection points form the vertices of a Penrose rhomb tiling. These vertices are then globally scaled and rotated to define <b>deployment positions</b> for floating modules in a wave-energy farm or coastal-protection array.Crucially, the Penrose tiling is <b>not fixed</b>: the parameters R_grid and γₖ are <b>design variables</b> that can be adjusted to generate different Penrose patches, i.e. different quasicrystal phases and scales of the farm layout.2. Graph Representation and Hydrodynamic CouplingFor each Penrose-based layout, a <b>graph</b> is constructed:Nodes correspond to floating modules at Penrose vertices.Edges represent hydrodynamic or structural connections between modules, defined for example by:Delaunay triangulation on the module positions; and/orA distance-based adjacency criterion.This graph is used to:Define a simple multi-body wave interaction model, where each module’s motion and energy absorption is influenced by neighbors according to the edges; andSupport later machine-learning surrogates that operate directly on the graph.The farm is evaluated under a <b>wave spectrum</b> (multiple frequencies and directions), producing at least:A <b>wave-energy absorption metric</b>, e.g. spectrum-averaged absorbed power; andA <b>wave-transmission metric</b>, measuring how much wave energy reaches a virtual shoreline behind the array.3. Micro-Scale Penrose “Skins” for Solar and CoolingEach floating module includes a <b>micro-structured surface layer</b> whose pattern is also derived from Penrose or aperiodic tiling concepts at micro/nano scales. The layer is characterized by a small set of design parameters (e.g. feature size, height, fill fraction, and material code).This Penrose-patterned surface layer is designed to affect at least:<b>Solar energy harvesting</b> (e.g. by improving photovoltaic absorption); and<b>Radiative cooling</b> (e.g. by increasing emissivity in a relevant infrared window).For system-level design, the detailed electromagnetics of the micro-structure may be summarized by surrogate functions that map the micro parameters to:A <b>module-level solar efficiency</b>; andA <b>module-level cooling gain</b>, which are aggregated to farm-scale metrics.4. Multi-Objective Climate-Resilience PerformanceThe overall performance of a Penrose wave farm is evaluated using multiple metrics, including at least:Wave energy absorption,Wave transmission toward the coast,Solar energy harvesting,Thermal cooling benefit, andA cost or complexity measure (e.g. number of modules and connections).A single scalar objective function can be formed as a weighted combination of these metrics to support scalar optimization, or they can be treated as separate objectives in a multi-objective setting.5. Graph Neural Network Surrogate for Penrose FarmsEach Penrose-based farm is naturally represented as a <b>graph</b> with:Node features encoding at least:module position,micro-scale surface parameters, andoptionally, a Penrose hierarchy indicator or other quasicrystal-specific feature;Edge structure from the farm adjacency; andGraph-level features representing the ambient wave climate.A <b>graph neural network (GNN)</b> is trained on a dataset of such farms, where the target outputs are the physically-computed performance metrics (wave energy, transmission, solar energy, cooling). The GNN thus becomes a <b>surrogate model</b> that approximates the mapping:(Penrose layout + micro skins + climate) → performance metrics.This surrogate can infer performance metrics much faster than full physics simulation.6. Evolutionary Optimization over Penrose Phase, Scale, and SkinsA <b>genome</b> encoding a candidate design may include:Penrose macro parameters (R_grid and γₖ) that define the quasicrystal layout,Macro farm parameters (global scale, rotation, adjacency radius when used), andMicro skin parameters (for the Penrose-patterned surface of the modules).An evolutionary or other search algorithm operates on a population of genomes, using either:The full physics-based evaluation, orThe GNN surrogate as the primary evaluator, optionally with periodic physics-based evaluations for validation.In this manner, the algorithm explores a <b>family of Penrose tilings and micro-structures</b> to find layouts that improve wave-energy extraction, reduce wave transmission toward the coast, increase solar harvesting and cooling, and manage cost.7. Application to Climate-Resilient InfrastructureThe described framework is particularly suitable for:<b>Coastal and island regions</b> (e.g. in Oceania) facing rising sea levels, stronger wave climates, and heat stress;Deployments where a single infrastructure must simultaneously:protect shorelines,generate energy from waves,generate energy from sunlight, andpassively cool surfaces or enclosed volumes.The key distinguishing aspects of this disclosure are:The use of <b>true Penrose quasicrystal tilings</b> as the macro layout for floating wave-energy farms;The treatment of <b>Penrose phase and scale parameters (R_grid, γₖ)</b> as <b>evolvable design variables</b>, not fixed decorations;The combination of <b>macro Penrose layout, micro Penrose skins, and a GNN surrogate</b> in a unified optimization framework.This disclosure is intended to establish these concepts as prior art and to prevent exclusive patenting of the general approach by third parties.<i>End of disclosure.</i><br> Quasicrystal ; Penrose tiling ; Intersection (aeronautics) ; Scalar (mathematics) ; Triangulation ; Graph ; Offset (computer science) Quasicrystal Structures and Properties ; Advanced Materials and Mechanics ; Marine and coastal plant biology