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This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks (FI-PINNs). In our previous work \cite{gao2022failure}, we have presented an adaptive sampling framework by using the…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from the sparse codes. We verify that the new…
Iterative algorithms are widely used in digital signal processing applications. With the case study of radio astronomy calibration processing, this work contributes towards revealing and exploiting the intrinsic error resilience of…
This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling…
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
In this paper, incremental adaptive mechanisms are presented and characterized, to provide design hints for the development of continuous-time adaptive systems. The comparison with the conventional integral adaptive systems indicates that…
In this paper, we study the power iteration algorithm for the spiked tensor model, as introduced in [44]. We give necessary and sufficient conditions for the convergence of the power iteration algorithm. When the power iteration algorithm…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
The analysis of signal-to-interference ratios (SIRs) in wireless networks is instrumental to derive important performance metrics, including reliability, throughput, and delay. While a host of results on SIR distributions are now available,…
The characterization of multicomponent signals with a particular emphasis on musical and communication signals is one of the problems studied in the dissertation. In order to provide an efficient analysis of the multicomponent signals, the…
The recent development in analog computation is reviewed in this paper. Analog computation was used in many applications where power and energy efficiency is of paramount importance. It is shown that by using innovative architecture and…
Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive…
We report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.
Structural models that admit multiple reduced forms, such as game-theoretic models with multiple equilibria, pose challenges in practice, especially when parameters are set-identified and the identified set is large. In such cases,…
Integration of large-scale renewable energy sources and increasing uncertainty has drastically changed the dynamics of power system and has consequently brought various challenges. Rapid transient stability assessment of modern power system…
Accurately modeling power distribution grids is crucial for designing effective monitoring and decision making algorithms. This paper addresses the partial observability issue of data-driven distribution modeling in order to improve the…
We present theoretical results and experiments with parallel algorithms for computing an adaptive, online control with the objective of attenuating a power grid cascading failure.
Algorithms for signal recovery in compressed sensing (CS) are often improved by stabilization techniques, such as damping, or the less widely known so-called fractional approach, which is based on the expectation propagation (EP) framework.…
Independent Component Analysis (ICA) is a dimensionality reduction technique that can boost efficiency of machine learning models that deal with probability density functions, e.g. Bayesian neural networks. Algorithms that implement…