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math.AP2019★ 4 cited
Physics-Informed Machine Learning with Conditional Karhunen-Loève Expansions
Alexandre M. Tartakovsky, David A. Barajas-Solano, Qizhi He
We present a new physics-informed machine learning approach for the inversion of PDE models with heterogeneous parameters. In our approach, the space-dependent partially-observed p…
math.AP2018
Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks
Alexandre M. Tartakovsky, Carlos Ortiz Marrero, Paris Perdikaris +2
We present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) mod…