A Conditional Neural Operator Approach for Resolution-Flexible and Parameter-Controlled Gravity Forward Modelling

We present a novel approach to gravity forward modeling using conditional neural operators that establishes a forward generative model from the basin models and hyperparameters (reference basement depth, etc.) to gravity anomaly. Our methodology introduces an innovative adaptive embedding mechanism where scalar hyperparameters are first embedded into a 32-dimensional space and then adaptively expanded to match the dimensions of the basin depth model, enabling effective fusion with basin depth model data. Subsequently, Fourier Convolution Layers are employed to transform the fused data into gravity anomalies. The model demonstrates superior performance compared to existing convolutional neural networks on the test dataset, showcasing improved accuracy in capturing complex geological structures and their gravity responses. A key advantage of our architectural design is that it not only preserves the super-resolution capability of conventional neural operators but also enables controlled generation through different hyperparameters. This dual capability allows for both resolution-flexible modeling and parameter-controlled generation, while training on low-resolution data and producing high-resolution outputs, significantly reducing training data requirements and computational costs. The model's adaptive architecture effectively bridges the resolution gap between training and application scenarios, offering a practical solution for real-world geological surveys. Our results suggest that this approach could substantially improve the accessibility and applicability of gravity forward modeling in various geological settings, particularly in regions with limited high-resolution training data.