A Test-Time Learning Approach to Reparameterize the Geophysical Inverse Problem with a Convolutional Neural Network

• URL: http://arxiv.org/abs/2312.04752v2
• Date: Tue, 9 Jul 2024 09:06:34 GMT
• Title: A Test-Time Learning Approach to Reparameterize the Geophysical Inverse Problem with a Convolutional Neural Network
• Authors: Anran Xu, Lindsey J. Heagy,
• Abstract summary: Explicit regularization is often used, but there are opportunities to explore the implicit regularization effects that are inherent in a Neural Network structure. Researchers have discovered that the Convolutional Neural Network (CNN) architecture inherently enforces a regularization. In this study, we examine the applicability of this implicit regularization to geophysical inversions.
• Score: 1.7396556690675236
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Regularization is critical for solving ill-posed geophysical inverse problems. Explicit regularization is often used, but there are opportunities to explore the implicit regularization effects that are inherent in a Neural Network structure. Researchers have discovered that the Convolutional Neural Network (CNN) architecture inherently enforces a regularization that is advantageous for addressing diverse inverse problems in computer vision, including de-noising and in-painting. In this study, we examine the applicability of this implicit regularization to geophysical inversions. The CNN maps an arbitrary vector to the model space. The predicted subsurface model is then fed into a forward numerical simulation to generate corresponding predicted measurements. Subsequently, the objective function value is computed by comparing these predicted measurements with the observed measurements. The backpropagation algorithm is employed to update the trainable parameters of the CNN during the inversion. Note that the CNN in our proposed method does not require training before the inversion, rather, the CNN weights are estimated in the inversion process, hence this is a test-time learning (TTL) approach. In this study, we choose to focus on the Direct Current (DC) resistivity inverse problem, which is representative of typical Tikhonov-style geophysical inversions (e.g. gravity, electromagnetic, etc.), to test our hypothesis. The experimental results demonstrate that the implicit regularization can be useful in some DC resistivity inversions. We also provide a discussion of the potential sources of this implicit regularization introduced from the CNN architecture and discuss some practical guides for applying the proposed method to other geophysical methods.

Related papers

• A predictive physics-aware hybrid reduced order model for reacting flows [65.73506571113623]
  A new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. The number of degrees of freedom is reduced from thousands of temporal points to a few POD modes with their corresponding temporal coefficients. Two different deep learning architectures have been tested to predict the temporal coefficients.
  arXiv  Detail & Related papers  (2023-01-24T08:39:20Z)
• Transformer Meets Boundary Value Inverse Problems [4.165221477234755]
  Transformer-based deep direct sampling method is proposed for solving a class of boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and reconstructed images.
  arXiv  Detail & Related papers  (2022-09-29T17:45:25Z)
• Convolutional Dictionary Learning by End-To-End Training of Iterative Neural Networks [3.6280929178575994]
  In this work, we construct an INN which can be used as a supervised and physics-informed online convolutional dictionary learning algorithm. We show that the proposed INN improves over two conventional model-agnostic training methods and yields competitive results also compared to a deep INN.
  arXiv  Detail & Related papers  (2022-06-09T12:15:38Z)
• On feedforward control using physics-guided neural networks: Training cost regularization and optimized initialization [0.0]
  Performance of model-based feedforward controllers is typically limited by the accuracy of the inverse system dynamics model. This paper proposes a regularization method via identified physical parameters. It is validated on a real-life industrial linear motor, where it delivers better tracking accuracy and extrapolation.
  arXiv  Detail & Related papers  (2022-01-28T12:51:25Z)
• Revisiting Transformation Invariant Geometric Deep Learning: Are Initial Representations All You Need? [80.86819657126041]
  We show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks.
  arXiv  Detail & Related papers  (2021-12-23T03:52:33Z)
• Robust lEarned Shrinkage-Thresholding (REST): Robust unrolling for sparse recover [87.28082715343896]
  We consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. We design a new robust deep neural network architecture by applying algorithm unfolding techniques to a robust version of the underlying recovery problem. The proposed REST network is shown to outperform state-of-the-art model-based and data-driven algorithms in both compressive sensing and radar imaging problems.
  arXiv  Detail & Related papers  (2021-10-20T06:15:45Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Physical invariance in neural networks for subgrid-scale scalar flux modeling [5.333802479607541]
  We present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs) We show that the proposed transformation-invariant NN model outperforms both purely data-driven ones and parametric state-of-the-art subgrid-scale models.
  arXiv  Detail & Related papers  (2020-10-09T16:09:54Z)
• Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example [0.0]
  Theory-guided Neural Network (TgNN) is constructed as a deep-learning surrogate for problems with uncertain model parameters. Direct-deep-learning-inversion methods, in which TgNN constrained with geostatistical information, is proposed for direct inverse modeling.
  arXiv  Detail & Related papers  (2020-07-28T15:31:07Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Rectified Linear Postsynaptic Potential Function for Backpropagation in Deep Spiking Neural Networks [55.0627904986664]
  Spiking Neural Networks (SNNs) usetemporal spike patterns to represent and transmit information, which is not only biologically realistic but also suitable for ultra-low-power event-driven neuromorphic implementation. This paper investigates the contribution of spike timing dynamics to information encoding, synaptic plasticity and decision making, providing a new perspective to design of future DeepSNNs and neuromorphic hardware systems.
  arXiv  Detail & Related papers  (2020-03-26T11:13:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.