Physics-Informed Neural Networks with SIMP Hot-Starting for Nonlinear Structural Analysis in Architectural Geometry Optimization

The intersection of computational design and structural engineering has significantly advanced architectural capabilities, enabling the creation of geometrically complex, high-performance structures. However, nonlinear structural analysis, essential for real-world optimization, remains computationally intensive, with traditional finite element methods (FEM) struggling to balance accuracy and efficiency. This research introduces a novel Physics-Informed Neural Networks with SIMP hot-starting Topology Optimization (PINNSTO) framework that addresses these challenges while achieving superior optimization outcomes. PINNSTO integrate physical laws directly into neural network loss functions, enabling accurate solutions without extensive labeled data. Our approach employs sinusoidal activation functions that significantly enhance boundary definition and structural representation capabilities, creating designs that are both mathematically optimal and more manufacturable for architectural applications. With SIMP hot-starting strategy, this framework effectively captures nonlinear behaviors crucial for evaluating complex architectural forms. Benchmark validations demonstrate 14–23% compliance reduction compared to traditional methods, with consistently smoother boundary definitions. Notably, the PINNSTO approach successfully converges for nonlinear problems, while maintaining comparable computational efficiency. It eliminates meshing errors and handles irregular geometries seamlessly—critical advantages for architectural applications. The implementation efficiently balances performance gains with computational costs, requiring only marginally more processing time. This research establishes PINNSTO as a robust foundation for architectural structural analysis, enabling simultaneous consideration of performance, material efficiency, and aesthetic intent in contemporary design challenges, particularly for applications involving additive manufacturing and complex material behaviors. By combining enhanced optimization capabilities with physical fidelity, PINNSTO offer a transformative approach to performance-driven design methodologies for sustainable, efficient architectural forms.