Machine Learning and Chaos Theory in Agriculture

Autor: Sebastian Raubitzek und Thomas Neubauer

Machine Learning techniques such as neural networks are today’s state of the art when it comes to regression analysis or time series prediction. The results in various disciplines are encouraging, and we, therefore, aim to use machine learning approaches in agriculture. There have, of course, been applications of machine learning in agriculture in the past, and to give an overview of its applicability, we name a few and refer to [Liakos et al., 2018] for a scienti c review of the topic. Common applications of machine learning in agriculture are:

• Yield prediction
• Disease detection
• Species recognition
• Water management

Further, in agricultural sciences, one has to deal with many complex phenomena, such as weather, water distributions, plant growth, etc. As this inherent complexity sometimes leads to unexpected results and makes prediction tasks difficult, we want to take the system’s complexity (or the chaotic behavior) into account for our analysis. For this reason, we want to employ tools that have been developed to measure the complexity of data or to estimate the chaotic behavior of systems. The practice of dealing with complexity or non-linear behavior is commonly referred to as chaos theory or non-linear dynamics1.
The hypothesis here is that combining machine learning with chaos theory will improve the overall applicability of arti cial intelligence in agriculture. We, therefore, propose the following ideas to be used when it comes to machine learning predictions of complex, and especially agricultural systems, Raubitzek and Neubauer, 2020:

1Here, we refer to the Book by Sakai, (Sakai, 2001), which lists several ideas and applications on how to use chaos theory in agriculture.

1. Filtering and processing raw data using methods from chaos theory.
2. Enriching meager data sets using di fferent interpolation techniques and chaos theory methods.
3. Filtering results depending on their complexity or chaoticity to improve results.

Given these ideas, we developed a fractal interpolation method based on the inherent complexity of the data under study and tested it to be using for machine learning time series predictions², (Raubitzek and Neubauer, 2021). Contrary to traditional interpolation techniques such as linear or polynomial interpolation, fractal interpolation is not based on a functional approach but uses iterative functions systems to generate new data points. The idea of a fractal interpolation is shown in Figure 1.

²To be speci c, we tested the predictability of fractal interpolated time series data using a long short term memory (LSTM) neural network.

Figure 1: Original and fractal interpolated Austrian wheat yields data. Only a fraction of the whole data is shown so that the fractal interpolation can clearly
be seen..

Given these ideas we have been able to signi cantly improve the test fit³ of a long short term memory (LSTM) neural network, shown in Figure 2.

 ³Note that this is not yet a prediction into the future, but a fi t on the test data, i.e. the data after the purple line.

Figure 2: Top: Test fit on non-interpolated data, Bottom: Test fit on fractal interpolated data..

Currently, work is done on developing complexity-based fi lters to further improve machine learning predictions. The results are encouraging, and we are looking forward on publishing our findings. The next steps will then be to find suitable real-life data  sets/scenarios to apply our approaches and find other scenarios for machine learning and chaos theory to be combined in an agricultural context.

Cite this post as::
S. Raubitzek und T. Neubauer,Machine Learning and Chaos Theory in Agriculture[Webblog]. Online-Publikation: „“, 2020.

[Liakos et al., 2018] Liakos, K. G., Busato, P., Moshou, D., Pearson, S., and Bochtis, D. (2018). Machine Learning in Agriculture: A Review. Sensors, 18(8).
[Raubitzek and Neubauer, 2020] Raubitzek, S. and Neubauer, T. (2020). Machine Learning and Chaos Theory in Agriculture. ERCIM News, 122.
[Raubitzek and Neubauer, 2021] Raubitzek, S. and Neubauer, T. (2021). A fractal interpolation approach to improve neural network predictions for diff cult time series data. Expert Systems with Applications, 169:114474.
[Sakai, 2001] Sakai, K. (2001). Nonlinear Dynamics and Chaos in Agricultural Systems. Elsevier Science, Amsterdam, 1 edition.Quellen: