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Randomized Physics-Informed Machine Learning for Uncertainty Quantification in High-Dimensional Inverse Problems
Uncertainty in the inverse solution is quantified in terms of the posterior distribution of CKLE coefficients, and we sample the posterior by solving a randomized PICKLE minimization problem, formulated by adding zero-mean Gaussian perturbations in the PICKLE loss function.
Physics-informed machine learning
Uncertainty Quantification
Physics-Informed Neural Network Method for Parabolic Differential Equations with Sharply Perturbed Initial Conditions
We propose a normalized form of ADE where the initial perturbation of the solution does not decrease in amplitude and demonstrate that this normalization significantly reduces the PINN approximation error.
