This paper focuses on the hypothesis of optimizing time series predictions
using fractal interpolation techniques. In general, the accuracy of machine
learning model predictions is closely related to the quality and quantitative
aspects of the data used, following the principle of \textit{garbage-in,
garbage-out}. In order to quantitatively and qualitatively augment datasets,
one of the most prevalent concerns of data scientists is to generate synthetic
data, which should follow as closely as possible the actual pattern of the
original data.
This study proposes three different data augmentation strategies based on
fractal interpolation, namely the \textit{Closest Hurst Strategy},
\textit{Closest Values Strategy} and \textit{Formula Strategy}. To validate the
strategies, we used four public datasets from the literature, as well as a
private dataset obtained from meteorological records in the city of Brasov,
Romania. The prediction results obtained with the LSTM model using the
presented interpolation strategies showed a significant accuracy improvement
compared to the raw datasets, thus providing a possible answer to practical
problems in the field of remote sensing and sensor sensitivity. Moreover, our
methodologies answer some optimization-related open questions for the fractal
interpolation step using \textit{Optuna} framework.

本文通过使用分形插值技术对时间序列预测进行了优化假设，提出了三种不同的基于分形插值的数据增强策略，并通过使用 LSTM 模型验证了这些策略对预测结果的显著改善，从而回答了一些与优化相关的分形插值步骤的开放性问题。

在预测精度优化背景下的分形插值

Fractal interpolation in the context of prediction accuracy optimization

Prediction of dynamic environmental variables in unmonitored sites remains a
long-standing challenge for water resources science. The majority of the
world's freshwater resources have inadequate monitoring of critical
environmental variables needed for management. Yet, the need to have widespread
predictions of hydrological variables such as river flow and water quality has
become increasingly urgent due to climate and land use change over the past
decades, and their associated impacts on water resources. Modern machine
learning methods increasingly outperform their process-based and empirical
model counterparts for hydrologic time series prediction with their ability to
extract information from large, diverse data sets. We review relevant
state-of-the art applications of machine learning for streamflow, water
quality, and other water resources prediction and discuss opportunities to
improve the use of machine learning with emerging methods for incorporating
watershed characteristics into deep learning models, transfer learning, and
incorporating process knowledge into machine learning models. The analysis here
suggests most prior efforts have been focused on deep learning learning
frameworks built on many sites for predictions at daily time scales in the
United States, but that comparisons between different classes of machine
learning methods are few and inadequate. We identify several open questions for
time series predictions in unmonitored sites that include incorporating dynamic
inputs and site characteristics, mechanistic understanding and spatial context,
and explainable AI techniques in modern machine learning frameworks.

预测未监测站点中的动态环境变量是水资源科学领域长期存在的挑战，使用机器学习方法对水文时间序列进行预测能够从大量多样的数据集中提取信息，并提出了几个开放问题，包括如何将动态输入和站点特征、机制性理解和空间背景以及可解释的人工智能技术融入现代机器学习框架中。