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physics.data-an2023
An information field theory approach to Bayesian state and parameter estimation in dynamical systems
Kairui Hao, Ilias Bilionis
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they…
physics.data-an2019
Simulator-free Solution of High-Dimensional Stochastic Elliptic Partial Differential Equations using Deep Neural Networks
Sharmila Karumuri, Rohit Tripathy, Ilias Bilionis +1
Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parame…