Related papers: TNet: A Model-Constrained Tikhonov Network Approac…
Recovering a function or high-dimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel…
Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…
Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…
Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence…
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…
Deep learning (DL) has achieved great success in many applications, but it has been less well analyzed from the theoretical perspective. The unexplainable success of black-box DL models has raised questions among scientists and promoted the…
Deep-learning has achieved good performance and shown great potential for solving forward and inverse problems. In this work, two categories of innovative deep-learning based inverse modeling methods are proposed and compared. The first…
Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of borehole logging…
In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…
Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional,…
Deep Learning (DL) has shown remarkable results in solving inverse problems in various domains. In particular, the Tikhonet approach is very powerful to deconvolve optical astronomical images (Sureau et al. 2020). Yet, this approach only…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve…
We propose a non-stationary iterated network Tikhonov (iNETT) method for the solution of ill-posed inverse problems. The iNETT employs deep neural networks to build a data-driven regularizer, and it avoids the difficult task of estimating…
Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT…
Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but…
Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…