Interpretable neural basis approximation for periodic cellular surfaces through analytic primitive mixtures

Nature-inspired cellular surfaces ( e.g. , Triply Periodic Minimal Surfaces or TPMS) are known as a versatile source of architected material designs for various applications ( e.g. , tissue engineering, mechanical engineering) due to their exceptional geometric and mechanical attributes. However, finding effective geometric modeling methods for those cellular surfaces remains one of the field’s longstanding, fundamental, open research problems. While different strategies, such as parametric, implicit, and boundary methods, have been successfully developed to mimic and approximate those intricate surfaces with nodal coordinates, these mainstream existing approaches can only generate limited types of cellular surfaces due to either topological complexity ( i.e. , high genus) or a limited set of identified functions ( e.g. , implicit functions). Fundamentally, current methods lack a mechanism to approximate complex periodic surfaces using a compact, interpretable basis. Just as Fourier transforms decompose signals into sine waves, our goal is to decompose cellular structures into weighted mixtures of analytic primitives. Thus, in this work, we leverage a deep learning model by introducing a hybrid generative parameterization framework that learns a compact, global representation for 3D Signed Distance fields (SDFs) by projecting complex geometries onto a learned basis of analytic primitives. Our model has employed a 3D convolutional encoder to extract latent features from input SDF volumes and decodes them into physically interpretable parameters, including fill-fraction factors, periodicity exponents, and soft mixture weights, over a list of complex SDF candidate functions. Such a design enables the model to perform spectral approximation of complex structural motifs directly in function space. We evaluated our model on four datasets of synthetic cellular surfaces and TPMS, and our method shows high-fidelity reconstructions. Furthermore, we demonstrate that our neural inference method achieves a ∼ 636x speedup compared to direct parameter optimization, enabling real-time design exploration. Our parametric approach offers an efficient and interpretable parameterization pipeline for CPCS, facilitating downstream tasks in simulation, design optimization, and digital manufacturing of cellular materials. • A novel hybrid implicit representation for complex periodic geometries is proposed. • The model combines a library of analytic primitives with a dual-encoder neural network. • It predicts physically interpretable parameters like fill-fraction, periodicity, and mixture weights. • Achieves high-fidelity reconstruction of complex Cubic Periodic Cellular Surfaces(CPCS). • Demonstrates strong performance on diverse datasets, including Triply Periodic Minimal Surfaces (TPMS).