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Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

Classical Transformer-based line segment detection methods have delivered impressive results. However, we observe that some accurately detected line segments are assigned low confidence scores during prediction, causing them to be ranked…

In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the…

A long-standing challenge in tomography is the 'missing wedge' problem, which arises when the acquisition of projection images within a certain angular range is restricted due to geometrical constraints. This incomplete dataset results in…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

Diffusion MRI (dMRI) provides the ability to reconstruct neuronal fibers in the brain, $\textit{in vivo}$, by measuring water diffusion along angular gradient directions in q-space. High angular resolution diffusion imaging (HARDI) can…

Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative,…

The lack of interpretability and trust is a much-criticised feature of deep neural networks. In fully connected nets, the signalling between inner layers is scrambled because backpropagation training does not require perceptrons to be…

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…

Non-linear dimensionality reduction can be performed by \textit{manifold learning} approaches, such as Stochastic Neighbour Embedding (SNE), Locally Linear Embedding (LLE) and Isometric Feature Mapping (ISOMAP). These methods aim to produce…

For reliability, it is important that the predictions made by machine learning methods are interpretable by human. In general, deep neural networks (DNNs) can provide accurate predictions, although it is difficult to interpret why such…

We assess a neural network (NN) method for reconstructing 3D cosmological density and velocity fields (target) from discrete and incomplete galaxy distributions (input). We employ second-order Lagrangian Perturbation Theory to generate a…

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

Blind super-resolution methods based on stable diffusion showcase formidable generative capabilities in reconstructing clear high-resolution images with intricate details from low-resolution inputs. However, their practical applicability is…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

In adaptive control theory, the dynamic regressor extension and mixing (DREM) procedure has become widespread as it allows one to describe major of adaptive control problems in unified terms of the parameter estimation problem of a…

Channel estimation poses significant challenges in millimeter-wave massive multiple-input multiple-output systems, especially when the base station has fewer radio-frequency chains than antennas. To address this challenge, one promising…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…