Conformal Prediction on Quantifying Uncertainty of Dynamic Systems

TL;DR

This paper introduces conformal prediction to quantify uncertainty in dynamic systems, providing theoretical guarantees and comparing it with other methods like Monte Carlo Dropout and Ensemble on PDE datasets.

Contribution

It applies conformal prediction to dynamical systems uncertainty assessment, offering a systematic approach supported by theoretical guarantees.

Findings

Conformal prediction effectively quantifies uncertainty in physical data.

Compared conformal prediction with Monte Carlo Dropout and Ensemble methods.

Demonstrated the method's effectiveness on PDE datasets for time-series tasks.

Abstract

Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure reliability. However, there is still a relative lack of systematic assessment of the uncertainties, particularly the uncertainties of the physical data. Our motivation is to introduce conformal prediction into the uncertainty assessment of dynamical systems, providing a method supported by theoretical guarantees. This paper uses the conformal prediction method to assess uncertainties with benchmark operator learning methods. We have also compared the Monte Carlo Dropout and Ensemble methods in the partial differential equations dataset, effectively evaluating uncertainty through straight roll-outs, making it ideal for time-series tasks.