MCMC Informed Neural Emulators for Uncertainty Quantification in Dynamical Systems

TL;DR

This paper introduces a novel approach using MCMC to incorporate parameter uncertainty directly into neural emulators, enabling efficient uncertainty quantification in dynamical systems without extensive sampling of network weights.

Contribution

The method decouples uncertainty quantification from neural network architecture by using MCMC on model parameters, reducing computation time and improving flexibility in emulating physical models.

Findings

Achieves uncertainty quantification comparable to physical models

Reduces training and evaluation time significantly

Provides a mathematical framework for performance analysis

Abstract

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model parameters is available. Here we study the common opposite situation, where direct screening or random sampling of model parameters leads to exhaustive training times and evaluations at unphysical parameter values. Our solution is to decouple uncertainty quantification from network architecture. Instead of sampling network weights, we introduce the model-parameter distribution as an input to network training via Markov chain Monte Carlo (MCMC). In this way, the surrogate achieves the same uncertainty quantification as the underlying physical model, but with substantially reduced computation time. The approach is fully agnostic with respect to the neural network choice. In our examples, we present a quantile emulator for prediction and a novel autoencoder-based ODE network emulator that can flexibly estimate different trajectory paths corresponding to different ODE model parameters. Moreover, we present a mathematical analysis that provides a transparent way to relate potential performance loss to measurable distribution mismatch.