Related papers: GS-PINN: Greedy Sampling for Parameter Estimation …
Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. The…
Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Active learning is increasingly adopted for expensive multi-objective combinatorial optimization problems, but it involves a challenging subset selection problem, optimizing the batch acquisition score that quantifies the goodness of a…
The randomized group-greedy method and its customized method for large-scale sensor selection problems are proposed. The randomized greedy sensor selection algorithm is applied straightforwardly to the group-greedy method, and a customized…
In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are obtained by solving a linear system by least squares. This…
In this work, we study Bayesian quantum parameter estimation given a finite number of uses of the process encoding one or more unknown physical quantities. For multiple uses, it is conventional to classify quantum metrological protocols as…
Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…
We study the problem of semi-supervised learning with Graph Neural Networks (GNNs) in an active learning setup. We propose GraphPart, a novel partition-based active learning approach for GNNs. GraphPart first splits the graph into disjoint…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
A key aspect for any greedy pursuit algorithm used in compressed sensing is a good support-set detection method. For distributed compressed sensing, we consider a setup where many sensors measure sparse signals that are correlated via the…
For the general parametric regression models with covariates contaminated with normal measurement errors, this paper proposes an accelerated version of the classical simulation extrapolation algorithm to estimate the unknown parameters in…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
This work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in-situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require…
Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…
Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a…
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…