Related papers: GS-PINN: Greedy Sampling for Parameter Estimation …
Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the…
The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…
The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…
Stochastic gradient descent (SGD) and projected stochastic gradient descent (PSGD) are scalable algorithms to compute model parameters in unconstrained and constrained optimization problems. In comparison with SGD, PSGD forces its iterative…
Neural networks often make predictions relying on the spurious correlations from the datasets rather than the intrinsic properties of the task of interest, facing sharp degradation on out-of-distribution (OOD) test data. Existing de-bias…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical…
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…
We propose a strategy for greedy sampling in the context of non-intrusive interpolation-based surrogate modeling for frequency-domain problems. We rely on a non-intrusive and cheap error indicator to drive the adaptive selection of the…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…
In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to…
In this paper, we consider the problem of collaboratively estimating the sparsity pattern of a sparse signal with multiple measurement data in distributed networks. We assume that each node makes Compressive Sensing (CS) based measurements…
We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of…
Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…
This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…
This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…
We consider the problem of finding sparse solutions to a system of underdetermined nonlinear system of equations. The methods are based on a Gauss-Newton approach with line search where the search direction is found by solving a linearized…