Conditional Pseudo-Reversible Normalizing Flow for Surrogate Modeling in Quantifying Uncertainty Propagation
This work addresses uncertainty quantification in surrogate modeling for physical systems, offering a method that simplifies implementation and avoids auxiliary sampling, though it appears incremental as it builds on existing normalizing flow techniques.
The paper tackles the problem of efficiently quantifying forward and inverse uncertainty propagation in physical models with additive noise by introducing a conditional pseudo-reversible normalizing flow that directly learns conditional probability density functions from input-output data without prior noise knowledge, achieving convergence to target densities as shown in benchmark tests and a real-world geologic carbon storage application.
We introduce a conditional pseudo-reversible normalizing flow for constructing surrogate models of a physical model polluted by additive noise to efficiently quantify forward and inverse uncertainty propagation. Existing surrogate modeling approaches usually focus on approximating the deterministic component of physical model. However, this strategy necessitates knowledge of noise and resorts to auxiliary sampling methods for quantifying inverse uncertainty propagation. In this work, we develop the conditional pseudo-reversible normalizing flow model to directly learn and efficiently generate samples from the conditional probability density functions. The training process utilizes dataset consisting of input-output pairs without requiring prior knowledge about the noise and the function. Our model, once trained, can generate samples from any conditional probability density functions whose high probability regions are covered by the training set. Moreover, the pseudo-reversibility feature allows for the use of fully-connected neural network architectures, which simplifies the implementation and enables theoretical analysis. We provide a rigorous convergence analysis of the conditional pseudo-reversible normalizing flow model, showing its ability to converge to the target conditional probability density function using the Kullback-Leibler divergence. To demonstrate the effectiveness of our method, we apply it to several benchmark tests and a real-world geologic carbon storage problem.