Related papers: Let data talk: data-regularized operator learning …
Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…
Registration is the process that computes the transformation that aligns sets of data. Commonly, a registration process can be divided into four main steps: target selection, feature extraction, feature matching, and transform computation…
In recent years, deep learning methods have been extensively developed for inverse imaging problems (IIPs), encompassing supervised, self-supervised, and generative approaches. Most of these methods require large amounts of labeled or…
Deep reinforcement learning (DRL) has achieved significant breakthroughs in various tasks. However, most DRL algorithms suffer a problem of generalizing the learned policy which makes the learning performance largely affected even by minor…
Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…
Deep reinforcement learning (DRL) has seen several successful applications to process control. Common methods rely on a deep neural network structure to model the controller or process. With increasingly complicated control structures, the…
We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model…
Reaction-diffusion (RD) equations underpin pattern formation across chemistry, biology, and physics, yet learning stable operators that forecast their long-term dynamics from data remains challenging. Neural-operator surrogates provide…
Overparameterized neural networks can be highly accurate on average on an i.i.d. test set yet consistently fail on atypical groups of the data (e.g., by learning spurious correlations that hold on average but not in such groups).…
This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since…
This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model system identification as an inner problem and predictive…
Training neural networks is an optimization problem, and finding a decent set of parameters through gradient descent can be a difficult task. A host of techniques has been developed to aid this process before and during the training phase.…
Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…
Distributed training in deep learning (DL) is common practice as data and models grow. The current practice for distributed training of deep neural networks faces the challenges of communication bottlenecks when operating at scale, and…
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…
Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a…
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…
A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…
Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…