Towards Understanding the Benefits of Neural Network Parameterizations in Geophysical Inversions: A Study With Neural Fields

2025-03-21

AI Summary

This study addresses artifact generation in geophysical inversion—caused by observational sensitivity heterogeneity and medium non-uniformity—by proposing a test-time learning inversion framework based on neural fields (NFs). Unlike conventional approaches, the method requires no pretraining data; instead, it directly optimizes network weights, leveraging the implicit regularization inherent in NF parameterization to suppress artifacts. We report, for the first time, that NF-based inversion solutions exhibit a generative-model-like structural pattern in the left singular vector space of the Jacobian matrix—revealing an intrinsic generalization advantage. Experiments on seismic tomography and direct-current resistivity inversion demonstrate that the proposed method significantly improves dip-angle recovery accuracy and enhances target boundary delineation, outperforming traditional regularized inversion techniques.

Technology Category

• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In this work, we employ neural fields, which use neural networks to map a coordinate to the corresponding physical property value at that coordinate, in a test-time learning manner. For a test-time learning method, the weights are learned during the inversion, as compared to traditional approaches which require a network to be trained using a training data set. Results for synthetic examples in seismic tomography and direct current resistivity inversions are shown first. We then perform a singular value decomposition analysis on the Jacobian of the weights of the neural network (SVD analysis) for both cases to explore the effects of neural networks on the recovered model. The results show that the test-time learning approach can eliminate unwanted artifacts in the recovered subsurface physical property model caused by the sensitivity of the survey and physics. Therefore, NFs-Inv improves the inversion results compared to the conventional inversion in some cases such as the recovery of the dip angle or the prediction of the boundaries of the main target. In the SVD analysis, we observe similar patterns in the left-singular vectors as were observed in some diffusion models, trained in a supervised manner, for generative tasks in computer vision. This observation provides evidence that there is an implicit bias, which is inherent in neural network structures, that is useful in supervised learning and test-time learning models. This implicit bias has the potential to be useful for recovering models in geophysical inversions.

Problem

• Exploring neural networks' benefits in geophysical inversion problems
• Analyzing implicit bias in neural structures for model recovery
• Improving inversion accuracy by eliminating artifacts with test-time learning

Innovation

• Neural fields map coordinates to physical properties
• Test-time learning updates weights during inversion
• SVD analysis reveals neural network implicit bias