Conditional Pseudo-Reversible Normalizing Flow for Surrogate Modeling in
  Quantifying Uncertainty Propagation
Minglei Yang Pengjun Wang Ming Fan Dan Lu Yanzhao Cao Guannan Zhang
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.