Influence of database noises to machine learning for spatiotemporal chaos

TL;DR

This paper demonstrates that the accuracy of machine learning predictions for spatiotemporal chaos heavily depends on the quality of the training data, emphasizing the importance of noise-free datasets obtained via the CNS strategy.

Contribution

It reveals the significant impact of database noise on ML predictions of chaos and highlights the necessity of using clean data for reliable results, introducing a new perspective in ML research.

Findings

ML trained on clean data yields more accurate predictions.

Noisy data significantly degrades ML performance.

Clean numerical simulation (CNS) provides high-quality benchmark data.

Abstract

A new strategy, namely the "clean numerical simulation" (CNS), was proposed (J. Computational Physics, 418:109629, 2020) to gain reliable/convergent simulations (with negligible numerical noises) of spatiotemporal chaotic systems in a long enough interval of time, which provide us benchmark solution for comparison. Here we illustrate that machine learning (ML) can always give good enough fitting predictions of a spatiotemporal chaos by using, separately, two quite different training sets: one is the "clean database" given by the CNS with negligible numerical noises, the other is the "polluted database" given by the traditional algorithms in single/double precision with considerably large numerical noises. However, even in statistics, the ML predictions based on the "polluted database" are quite different from those based on the "clean database". It illustrates that the database noises have huge influences on ML predictions of some spatiotemporal chaos, even in statistics. Thus, we must use a "clean" database for machine learning of some spatiotemporal chaos. This surprising result might open a new door and possibility to study machine learning.