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Neural Topology Optimization Using B-Spline Positional Encoding
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DOI：10.1007/s11424-026-5391-5.png)
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Abstract
En 中文
Topology optimization offers lightweight and high-performance solutions for structural design. With the rapid advancement of neural networks, topology optimization methods leveraging neural architectures have gained increasing attention. Among these methods, positional encoding is crucial for enabling neural networks to capture high-frequency geometry features, making its integration into neural network-based optimization methods a promising direction for exploration. This paper focuses on positional encoding by introducing a spline-based positional encoding into the neural topology optimization framework, in which spatial coordinates are transformed using spline basis functions before being input into the neural network. The performance of different classic spline basis functions is comprehensively evaluated, including the Bézier spline, B-spline, and NURBS spline. Experimental results demonstrate that positional encoding based on quadratic B-spline basis functions yields the highest structural stiffness. To further validate the effectiveness of the proposed method, a comparative analysis is performed against Fourier and super-Gaussian positional encoding schemes. The results show that spline-based encoding outperforms both alternatives in terms of structural compliance in most cases. Moreover, the resulting topologies exhibit smooth boundaries, free from oscillations and superfluous geometric details.
Keywords:
Neural networks
spline basis functions
spline positional encoding
topology optimization
Journal
J
IF:
2.8
Papers:
23
Citations:
0
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