Learning on the Correct Class for Domain Inverse Problems of Gravimetry

Core Concepts

The author proposes learning on the correct class as a strategy to address the ill-posed inverse gravimetry problem, ensuring reliable solutions within specific constraints.

Abstract

In the study of inverse gravimetry, end-to-end learning approaches are explored to determine Earth's mass distribution. The reliability of these methods is questioned due to ill-posedness, leading to the proposal of learning on the correct class. By employing well-posedness theorems and unique solution constraints, a neural network architecture is designed for domain inverse problems of gravimetry. The approach involves mimicking level-set formulations and utilizing density-contrast functions to recover non-constant mass models efficiently. The content delves into the challenges posed by ill-posed inverse gravimetry problems and introduces a novel strategy of learning on the correct class. By restricting solutions within specific classes based on uniqueness theorems, reliable outcomes can be achieved. The proposed method involves designing neural networks that adhere to certain geometric constraints and utilize a priori information for accurate mass model recovery. Through numerical examples and theoretical frameworks, the efficacy and promise of this approach in geophysical explorations using gravity data are highlighted.

Stats

Given some a priori information of f and imposing certain geometric constraints on D, the domain inverse problem of gravimetry admits a unique solution. We build pairs of mass models and gravity data for training neural networks. The loss function for training includes terms measuring discrepancy between true model µs and neural-network output. Table 1 lists average values of PSNR and SSIM for reconstructions on test samples and salt models.

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Learning on the correct class for domain inverse problems of gravimetry

by Yihang Chen,... at arxiv.org 03-13-2024

https://arxiv.org/pdf/2403.07393.pdf

Deeper Inquiries

How does learning on the correct class impact generalization abilities in other scientific fields?

In various scientific fields, learning on the correct class can significantly enhance generalization abilities. By restricting solutions to a specific class based on well-posedness conditions or uniqueness theorems, the learned models are more likely to provide reliable and consistent results across different datasets. This approach ensures that the solutions generated by machine learning algorithms are not only accurate for the training data but also generalize well to unseen data. When applied in other scientific domains such as medical imaging, climate modeling, or material science, learning on the correct class helps mitigate overfitting issues and improves model robustness. By incorporating domain-specific constraints into the learning process, researchers can guide neural networks to focus on relevant features and structures within the data, leading to more interpretable and transferable models. Overall, leveraging correct classes in machine learning tasks outside of gravimetry promotes better generalization capabilities by encouraging models to capture essential patterns while avoiding spurious correlations or noise present in the data.

What potential drawbacks or limitations might arise from strictly adhering to correct classes in solving inverse problems?

While adhering strictly to correct classes when solving inverse problems offers several benefits like ensuring unique solutions and improving reliability, there are potential drawbacks and limitations associated with this approach: Limited Flexibility: Strict adherence to correct classes may limit the flexibility of models in capturing complex relationships present in real-world data. In some cases where true underlying structures deviate from predefined classes, this rigidity could lead to suboptimal solutions. Increased Computational Complexity: Defining narrow correct classes often requires additional computational resources for validation against uniqueness criteria or constraints. This increased complexity can hinder scalability when dealing with large datasets or high-dimensional spaces. Sensitivity to Assumptions: Correct classes rely heavily on assumptions about problem characteristics such as smoothness of functions or geometric properties of domains. If these assumptions do not hold true in practice due to noise or uncertainties, strict adherence may result in biased outcomes. Generalization Challenges: Over-reliance on predefined correct classes may impede model generalization beyond training scenarios since real-world variations might not always align perfectly with theoretical constructs.

How can deep learning strategies be adapted to address other ill-posed problems beyond gravimetry?

Deep learning strategies can be adapted effectively to address a wide range of ill-posed problems beyond gravimetry by incorporating domain knowledge and regularization techniques tailored specifically for each problem domain: Regularization Techniques: Implementing regularization methods like weight decay (L2 regularization), dropout layers, early stopping mechanisms help prevent overfitting and improve model stability when dealing with ill-posed problems. Domain-Specific Constraints: Introducing prior knowledge about problem characteristics through custom loss functions or network architectures enables deep learning models to adhere closely to desired solution spaces while handling ambiguity inherent in ill-posed settings. Data Augmentation: Generating synthetic training samples through data augmentation techniques such as rotation, scaling, cropping enhances model robustness against variations commonly encountered in ill-posed scenarios where limited observed information is available. 4** Hybrid Approaches:** Combining physics-based modeling with deep neural networks allows for hybrid approaches that leverage both empirical data-driven insights from deep learning frameworks along with analytical reasoning derived from traditional methodologies for tackling complex ill-posed challenges effectively.