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Modeling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned…

Neural decoding from electroencephalography (EEG) remains fundamentally limited by poor generalization to unseen subjects, driven by high inter-subject variability and the lack of large-scale datasets to model it effectively. Existing…

Diffusion probabilistic models have recently achieved remarkable success in generating high-quality images. However, balancing high perceptual quality and low distortion remains challenging in application of diffusion models in image…

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

Mesh denoising is a critical technology in geometry processing that aims to recover high-fidelity 3D mesh models of objects from their noise-corrupted versions. In this work, we propose a learning-based normal filtering scheme for mesh…

Variations of deep neural networks such as convolutional neural network (CNN) have been successfully applied to image denoising. The goal is to automatically learn a mapping from a noisy image to a clean image given training data consisting…

Variational data assimilation in ocean models depends on the ability to model general correlation operators in the presence of coastlines. Grid-point filters based on diffusion operators are widely used for this purpose, but come with a…

The fundamental principle of Graph Neural Networks (GNNs) is to exploit the structural information of the data by aggregating the neighboring nodes using a `graph convolution' in conjunction with a suitable choice for the network…

Diffusion has shown great success in improving accuracy of unsupervised image retrieval systems by utilizing high-order structures of image manifold. However, existing diffusion methods suffer from three major limitations: 1) they usually…

The recent emergence of diffusion models has significantly advanced the precision of learnable priors, presenting innovative avenues for addressing inverse problems. Since inverse problems inherently entail maximum a posteriori estimation,…

Atmospheric effects, such as turbulence and background thermal noise, inhibit the propagation of coherent light used in ON-OFF keying free-space optical communication. Here we present and experimentally validate a convolutional neural…

Diffusion models cannot enforce hard constraints, yet applications in the physical sciences demand exact satisfaction of conservation laws, boundary conditions, and observational consistency. In this work, we identify a corrector kernel…

Generative diffusion models trained on large-scale datasets have achieved remarkable progress in image synthesis. In favor of their ability to supplement missing details and generate aesthetically pleasing contents, recent works have…

Conditional density estimation (CDE) is the task of estimating the probability of an event conditioned on some inputs. A neural network (NN) can also be used to compute the output distribution for continuous-domain, which can be viewed as…

The extraction of geoelectric structural information from airborne transient electromagnetic(ATEM)data primarily involves data processing and inversion. Conventional methods rely on empirical parameter selection, making it difficult to…

We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…

With the goal of predicting the future rainfall intensity in a local region over a relatively short period time, precipitation nowcasting has been a long-time scientific challenge with great social and economic impact. The radar echo…

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 unfolding networks have recently gained popularity in the context of solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with…

Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…