MCMC Informed Neural Emulators for Uncertainty Quantification in Dynamical Systems

2026-03-11

AI Summary

This work proposes an MCMC-guided neural surrogate framework to address the limitations of conventional neural network surrogates in parameter uncertainty quantification, which typically rely on prior distributions and suffer from high computational costs and non-physical predictions due to direct sampling. By using posterior parameter distributions generated via Markov chain Monte Carlo (MCMC) as inputs to the surrogate model, the approach decouples uncertainty quantification from the neural architecture, thereby maintaining compatibility with arbitrary network structures. The framework further incorporates a quantile predictor and an autoencoded ODE network to flexibly capture physically consistent trajectories across varying parameters. Theoretical analysis establishes a link between distributional bias and performance degradation, demonstrating that the method significantly reduces computational overhead while preserving uncertainty quantification fidelity comparable to that of the original physical model.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• uncertainty quantification
• dynamical systems
• parameter sampling
• computational efficiency
• non-physical parameters

Innovation

• MCMC-informed emulator
• uncertainty quantification
• neural surrogate
• distribution-aware training
• ODE autoencoder