5 papers · 1 filter
Learning Chaotic Dynamics through Second-Order Geometric Supervision
Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh
Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics.…
From an Elementary Proof of Error Representation for Hermite Quadrature to a Rediscovery of Legendre Polynomials and Rodrigues Formula
Tan Bui-Thanh, Giancarlo Villatoro, C. G. Krishnanunni
We generalize two-point interpolatory Hermite quadrature to functions with available values and the first (n-1) derivatives at both end points. Armed with integration by parts in t…
A New Look at the Ensemble Kalman Filter for Inverse Problems: Duality, Non-Asymptotic Analysis and Convergence Acceleration
C G Krishnanunni, Jonathan Wittmer, Tan Bui-Thanh +1
This work presents new results and understanding of the Ensemble Kalman filter (EnKF) for inverse problems. In particular, using a Lagrangian dual perspective we show that EnKF can…
Improvements on uncertainty quantification with variational autoencoders
Andrea Tonini, Tan Bui-Thanh, Francesco Regazzoni +2
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. I…
A Divergence-Free and -Conforming Embedded-Hybridized DG Method for the Incompressible Resistive MHD equations
Jau-Uei Chen, Tamás L. Horváth, Tan Bui-Thanh
We present a divergence-free and -conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving…