Related papers: Inverse Problems, Deep Learning, and Symmetry Brea…

Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…

We propose a new method to tackle the mapping challenge from time-series data to spatial image in the field of seismic exploration, i.e., reconstructing the velocity model directly from seismic data by deep neural networks (DNNs). The…

In a physical neural system, learning rules must be local both in space and time. In order for learning to occur, non-local information must be communicated to the deep synapses through a communication channel, the deep learning channel. We…

Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning…

Modern deep learning models are highly overparameterized, resulting in large sets of parameter configurations that yield the same outputs. A significant portion of this redundancy is explained by symmetries in the parameter…

Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…

Symmetry is present throughout nature and continues to play an increasingly central role in physics and machine learning. Fundamental symmetries, such as Poincar\'{e} invariance, allow physical laws discovered in laboratories on Earth to be…

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…

Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems,…

Recent advances in meta-optics have enabled diverse functionalities in compact optical devices; however, conventional forward design approaches become inadequate as device complexity and scale grow. Inverse design offers a powerful…

The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions,…

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…

Deep metric learning aims to learn embeddings that contain semantic similarity information among data points. To learn better embeddings, methods to generate synthetic hard samples have been proposed. Existing methods of synthetic hard…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep…

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…

We propose an end-to-end deep learning framework that comprehensively solves the inverse wave scattering problem across all length scales. Our framework consists of the newly introduced wide-band butterfly network coupled with a simple…

Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based…