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We propose a kernel regression method to predict a target signal lying over a graph when an input observation is given. The input and the output could be two different physical quantities. In particular, the input may not be a graph signal…
In this paper we propose a real-time and robust solution to large-scale multiple rotation averaging. Until recently, Multiple rotation averaging problem had been solved using conventional iterative optimization algorithms. Such methods…
This work focuses on a compositional data-driven approach to verify incremental global asymptotic stability (delta-GAS) over interconnected homogeneous networks of degree one with unknown mathematical dynamics. Our proposed approach…
Seismic data noise processing is an important part of seismic exploration data processing, and the effect of noise elimination is directly related to the follow-up processing of data. In response to this problem, many authors have proposed…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
Self-supervised learning can significantly improve the performance of downstream tasks, however, the dimensions of learned representations normally lack explicit physical meanings. In this work, we propose a novel self-supervised approach…
This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and…
We build interpretable and lightweight transformer-like neural networks by unrolling iterative optimization algorithms that minimize graph smoothness priors -- the quadratic graph Laplacian regularizer (GLR) and the $\ell_1$-norm graph…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
We propose a novel iterative method to adapt a a graph to d-dimensional image data. The method drives the nodes of the graph towards image features. The adaptation process naturally lends itself to a measure of feature saliency which can…
Machine learning models are prone to capturing the spurious correlations between non-causal attributes and classes, with counterfactual data augmentation being a promising direction for breaking these spurious associations. However,…
In this paper, we propose an end-to-end graph learning framework, namely Iterative Deep Graph Learning (IDGL), for jointly and iteratively learning graph structure and graph embedding. The key rationale of IDGL is to learn a better graph…
This paper studies interpretability of convolutional networks by means of saliency maps. Most approaches based on Class Activation Maps (CAM) combine information from fully connected layers and gradient through variants of backpropagation.…
Adaptive inference is a promising technique to improve the computational efficiency of deep models at test time. In contrast to static models which use the same computation graph for all instances, adaptive networks can dynamically adjust…
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous…
We propose a convolutional neural network (CNN) denoising based method for seismic data interpolation. It provides a simple and efficient way to break though the lack problem of geophysical training labels that are often required by deep…
The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…