Neumann Series-based Neural Operator for Solving Inverse Medium Problem

• URL: http://arxiv.org/abs/2409.09480v1
• Date: Sat, 14 Sep 2024 16:54:30 GMT
• Title: Neumann Series-based Neural Operator for Solving Inverse Medium Problem
• Abstract summary: This study introduces a novel approach by integrating a Neumann series structure within a neural network framework. Experiments demonstrate that our methodology not only accelerates computations but also significantly enhances generalization performance.
• Score: 5.980803988596087
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively handle multiparameter inputs. Experiments demonstrate that our methodology not only accelerates computations but also significantly enhances generalization performance, even with varying scattering properties and noisy data. The robustness and adaptability of our framework provide crucial insights and methodologies, extending its applicability to a broad spectrum of scattering problems. These advancements mark a significant step forward in the field, offering a scalable solution to traditionally complex inverse problems.

Related papers

• Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems [9.254864022032747]
  Multiscale problems are notoriously difficult to tackle using traditional numerical methods.<n>This challenge is particularly pronounced in applications such as materials science, fluid dynamics, climate systems, chemical processes, and complex networks.<n>Recent neural operator models provide a promising data-driven alternative, but frequently struggle to achieve sufficient accuracy.
  arXiv  Detail & Related papers  (2026-07-14T09:41:49Z)
• Constraints Matrix Diffusion based Generative Neural Solver for Vehicle Routing Problems [16.541111954252397]
  We propose a novel fusion neural network framework that employs a discrete noise graph diffusion model to learn the underlying constraints of vehicle routing problems.<n>This work represents the first comprehensive experimental investigation of neural network model solvers across a 378-combinatorial space.
  arXiv  Detail & Related papers  (2026-03-08T10:03:34Z)
• Physics-Driven Neural Network for Solving Electromagnetic Inverse Scattering Problems [7.564377962527698]
  A new solution is proposed for inverse scattering problems (ISPs) using a physics-driven neural network (PDNN)<n>PDNN is trained only requiring the input of collected scattered fields and the computation of scattered fields corresponding to predicted solutions.<n>Results demonstrate that the proposed scheme has high reconstruction accuracy and strong stability, even when dealing with composite lossy scatterers.
  arXiv  Detail & Related papers  (2025-07-22T08:04:50Z)
• Data-driven approaches to inverse problems [12.614421935598317]
  Inverse problems serve as critical tools for visualizing internal structures beyond what is visible to the naked eye.<n>A more recent paradigm considers deriving solutions to inverse problems in a data-driven manner.<n>These notes offer an introduction to this data-driven paradigm for inverse problems.
  arXiv  Detail & Related papers  (2025-06-13T12:44:32Z)
• Error Feedback under $(L_0,L_1)$-Smoothness: Normalization and Momentum [56.37522020675243]
  We provide the first proof of convergence for normalized error feedback algorithms across a wide range of machine learning problems. We show that due to their larger allowable stepsizes, our new normalized error feedback algorithms outperform their non-normalized counterparts on various tasks.
  arXiv  Detail & Related papers  (2024-10-22T10:19:27Z)
• A Primal-dual algorithm for image reconstruction with ICNNs [3.4797100095791706]
  We address the optimization problem in a data-driven variational framework, where the regularizer is parameterized by an input- neural network (ICNN) While gradient-based methods are commonly used to solve such problems, they struggle to effectively handle nonsmoothness. We show that a proposed approach outperforms subgradient methods in terms of both speed and stability.
  arXiv  Detail & Related papers  (2024-10-16T10:36:29Z)
• A Guide to Stochastic Optimisation for Large-Scale Inverse Problems [4.926711494319977]
  optimisation algorithms are the de facto standard for machine learning with large amounts of data. We provide a comprehensive account of the state-of-the-art in optimisation from the viewpoint of inverse problems. We focus on the challenges for optimisation that are unique and are not commonly encountered in machine learning.
  arXiv  Detail & Related papers  (2024-06-10T15:02:30Z)
• An Unsupervised Deep Learning Approach for the Wave Equation Inverse Problem [12.676629870617337]
  Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters. Due to limitations in observation, limited shots or receivers, and random noise, conventional inversion methods are confronted with numerous challenges. We provide an unsupervised learning approach aimed at accurately reconstructing physical velocity parameters.
  arXiv  Detail & Related papers  (2023-11-08T08:39:33Z)
• Neural network analysis of neutron and X-ray reflectivity data: Incorporating prior knowledge for tackling the phase problem [141.5628276096321]
  We present an approach that utilizes prior knowledge to regularize the training process over larger parameter spaces. We demonstrate the effectiveness of our method in various scenarios, including multilayer structures with box model parameterization. In contrast to previous methods, our approach scales favorably when increasing the complexity of the inverse problem.
  arXiv  Detail & Related papers  (2023-06-28T11:15:53Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• On Robust Numerical Solver for ODE via Self-Attention Mechanism [82.95493796476767]
  We explore training efficient and robust AI-enhanced numerical solvers with a small data size by mitigating intrinsic noise disturbances. We first analyze the ability of the self-attention mechanism to regulate noise in supervised learning and then propose a simple-yet-effective numerical solver, Attr, which introduces an additive self-attention mechanism to the numerical solution of differential equations.
  arXiv  Detail & Related papers  (2023-02-05T01:39:21Z)
• To be or not to be stable, that is the question: understanding neural networks for inverse problems [0.0]
  In this paper, we theoretically analyze the trade-off between stability and accuracy of neural networks. We propose different supervised and unsupervised solutions to increase the network stability and maintain a good accuracy.
  arXiv  Detail & Related papers  (2022-11-24T16:16:40Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation [101.22379613810881]
  We consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive process. We propose a tractable approximation that allows us to scale our method to high-capacity neural network models.
  arXiv  Detail & Related papers  (2021-02-16T06:04:27Z)
• Differentiable Causal Discovery from Interventional Data [141.41931444927184]
  We propose a theoretically-grounded method based on neural networks that can leverage interventional data. We show that our approach compares favorably to the state of the art in a variety of settings.
  arXiv  Detail & Related papers  (2020-07-03T15:19:17Z)
• Total Deep Variation: A Stable Regularizer for Inverse Problems [71.90933869570914]
  We introduce the data-driven general-purpose total deep variation regularizer. In its core, a convolutional neural network extracts local features on multiple scales and in successive blocks. We achieve state-of-the-art results for numerous imaging tasks.
  arXiv  Detail & Related papers  (2020-06-15T21:54:15Z)

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.