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math.NA2020
Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
Wayne Isaac Tan Uy, Benjamin Peherstorfer
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by line…
math.NA2020
Neural network representation of the probability density function of diffusion processes
Wayne Isaac Tan Uy, Mircea Grigoriu
Physics-informed neural networks are developed to characterize the state of dynamical systems in a random environment. The neural network approximates the probability density funct…