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Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in…
Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…
Model-based deep learning methods such as loop unrolling (LU) and deep equilibrium model}(DEQ) extensions offer outstanding performance in solving inverse problems (IP). These methods unroll the optimization iterations into a sequence of…
It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of…
The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem. To overcome this, we propose a novel RNN…
Non-injective functions are not globally invertible. However, they can often be restricted to locally injective subdomains where the inversion is well-defined. In many settings a preferred solution can be selected even when multiple valid…
Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…
We introduce a new architecture called a conditional invertible neural network (cINN), and use it to address the task of diverse image-to-image translation for natural images. This is not easily possible with existing INN models due to some…
Inverse problems exist in a wide variety of physical domains from aerospace engineering to medical imaging. The goal is to infer the underlying state from a set of observations. When the forward model that produced the observations is…
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…
Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…
We develop a physics-informed neural networks (PINNs) framework for the inverse scattering problem in nuclear physics and apply it to the $P_{3/2}$ partial wave of neutron-alpha elastic scattering. The radial potential is represented by a…
We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible.…
Neural networks trained on visual data are well-known to be vulnerable to often imperceptible adversarial perturbations. The reasons for this vulnerability are still being debated in the literature. Recently Ilyas et al. (2019) showed that…
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…
Modern optimizing compilers are able to exploit memory access or computation patterns to generate vectorization codes. However, such patterns in irregular applications are unknown until runtime due to the input dependence. Thus, either…
Can regularization terms in the training of invertible neural networks lead to known Bayesian point estimators in reconstruction? Invertible networks are attractive for inverse problems due to their inherent stability and interpretability.…
Despite recent progress in our understanding of complex dynamic networks, it remains challenging to devisesufficiently accurate models to observe, control or predict the state of real systems in biology, economics or other fields. A largely…
The unfolding of detector effects is crucial for the comparison of data to theory predictions. While traditional methods are limited to representing the data in a low number of dimensions, machine learning has enabled new unfolding…