466 citations · 1.7k across the 54 of their papers we have counts for
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Solving differential equations with unknown constitutive relations as recurrent neural networks
Tobias Hagge, Panos Stinis, Enoch Yeung +1
We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variable…
Stochastic basis adaptation and spatial domain decomposition for PDEs with random coefficients
Ramakrishna Tipireddy, Panos Stinis, Alexandre Tartakovsky
We present a novel uncertainty quantification approach for high-dimensional stochastic partial differential equations that reduces the computational cost of polynomial chaos method…
Sliced-Inverse-Regression-Aided Rotated Compressive Sensing Method for Uncertainty Quantification
Xiu Yang, Weixuan Li, Alexandre Tartakovsky
Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this work, we use the sliced inverse regression (SIR)…
PDF estimation for power grid systems via sparse regression
Xiu Yang, David A. Barajas-Solano, W. Steven Rosenthal +1
We present a numerical approach for estimating the probability density function (PDF) of quantities of interest (QoIs) of power grid systems subject to uncertain power generation a…