# GeoSAE: A 3D Stratographic Modeling Method Driven by Geological Constraint
## 4 Discussion  
The modeling results indicate that the GeoSAE method excels in constructing 3D geological models that incorporate multiple unconformities and continuous stratigraphic interfaces. It is particularly effective in generating scalar field values that adhere to geological principles, even when handling noisy regional datasets. Although the stratigraphic sequence relationship loss and global smoothing loss contribute incrementally to model optimization, they provide crucial support for validating the model's effectiveness. Particularly in data-scarce areas, such as outcrop regions with limited profile data, these constraints offer significant improvements. They enable the integration of geological maps into the modeling process by sampling points within unit polygons and incorporating these points as constraints with weighting terms to guide the model toward results that better reflect geological structures. Figure 17: (**a**) Qp1x Xiuying Group stratigraphic surface constructed with a smoothness constraint weight of 0.1; (**b**) Qp1x Xiuying Group stratigraphic surface constructed with a smoothness constraint weight of 0.05; (**c**) Qp1x Xiuying Group stratigraphic surface constructed with a smoothness constraint weight of 0.01. Furthermore, the GeoSAE model effectively handles both internal and external constraints on stratigraphic relationships, demonstrating its potential to integrate new geological constraints. For example, the model automatically learns the optimal isosurface for each stratigraphic surface, thus overcoming the limitations of manually specified isosurfaces. This method is more flexible in adapting to complex geological structures, especially when modeling areas with varying or significant thickness changes. Compared to the limitations of manually specified isosurfaces in traditional methods, GeoSAE significantly enhances the expression of stratigraphic structures. Experimental results show that the Softplus function effectively captures high-frequency details in the data while avoiding unnatural folding features when generating structures with good geological representation. The ReLU activation function typically results in sharper geometric shapes, which may be more suitable for brittle structural environments, while the smoother geometric shapes produced by the Softplus function better align with the actual features of geological structures. Experimental results show that the Softplus function effectively captures high-frequency details in the data while avoiding unnatural folding features when generating structures with good geological representation. In contrast, while the ReLU activation function generates sharper geometric shapes, in certain cases, the model's fitting performance may be compromised, especially when higher stratigraphic smoothness is required. However, although the GeoSAE model performs excellently in fitting most stratigraphic surfaces, some layers (such as N1d and N2h) exhibit significant fitting errors. These errors may stem from the inherent complexity of the actual geological data, such as vertical folding of strata and erosional unconformities, which make it difficult for the model to fully capture the subtle variations in the strata. Moreover, while the global smoothing constraint reduces the impact of data noise to some extent, excessive smoothing weights may suppress important geological features in the strata, leading to overly smooth stratigraphic surfaces, which could affect the model's accuracy. Therefore, future research could further optimize the weight of the smoothing constraint to better balance the smoothness of the model with the retention of details. Overall, the GeoSAE method provides a new and effective approach for 3D geological modeling, excelling in handling complex geological structures and large-scale regional modeling. This method not only enhances the accuracy of modeling but also improves the model's adaptability to complex geological environments, offering important references for future geological modeling and data analysis.