Related papers: Transformer Meets Boundary Value Inverse Problems

Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular…

The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…

This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…

Current neural architectures lack a principled way to handle interchangeable tokens, i.e., symbols that are semantically equivalent yet distinguishable, such as bound variables. As a result, models trained on fixed vocabularies often…

Automated liver segmentation from radiology scans (CT, MRI) can improve surgery and therapy planning and follow-up assessment in addition to conventional use for diagnosis and prognosis. Although convolutional neural networks (CNNs) have…

Magnetic Resonance Imaging (MRI) is a powerful, non-invasive diagnostic tool; however, its clinical applicability is constrained by prolonged acquisition times. Whilst present deep learning-based approaches have demonstrated potential in…

Learning based methods are now ubiquitous for solving inverse problems, but their deployment in real-world applications is often hindered by the lack of ground truth references for training. Recent self-supervised learning strategies offer…

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…

Implicit Neural Representations (INRs) have emerged and shown their benefits over discrete representations in recent years. However, fitting an INR to the given observations usually requires optimization with gradient descent from scratch,…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

Retrosynthesis prediction is one of the fundamental challenges in organic synthesis. The task is to predict the reactants given a core product. With the advancement of machine learning, computer-aided synthesis planning has gained…

This paper introduces a new approach for solving electrical impedance tomography (EIT) problems using deep neural networks. The mathematical problem of EIT is to invert the electrical conductivity from the Dirichlet-to-Neumann (DtN) map.…

In this paper, we introduce deep learning technology to tackle two traditional low-level image processing problems, companding and inverse halftoning. We make two main contributions. First, to the best knowledge of the authors, this is the…

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these…

Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…

Many real-world problems can be naturally described by mathematical formulas. The task of finding formulas from a set of observed inputs and outputs is called symbolic regression. Recently, neural networks have been applied to symbolic…

Benefiting from powerful convolutional neural networks (CNNs), learning-based image inpainting methods have made significant breakthroughs over the years. However, some nature of CNNs (e.g. local prior, spatially shared parameters) limit…

Medical imaging is nowadays a pillar in diagnostics and therapeutic follow-up. Current research tries to integrate established - but ionizing - tomographic techniques with technologies offering reduced radiation exposure. Diffuse Optical…

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method…