# Deep Learning on time-variant Product Space

Arnault Pachot

► To cite this version:

Arnault Pachot. Deep Learning on time-variant Product Space. 11th International Academic Conference on Economics, Business, Technology and Social Sciences, European Institute for Research and Development, Nov 2022, Prague, Czech Republic. hal-03883391

HAL Id: hal-03883391

https://hal.science/hal-03883391

Submitted on 3 Dec 2022

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ATLAS
DES SYNERGIES PRODUCTIVES

# Deep Learning on
time-variant
Product Space

Arnault Pachot

Prague, November 5 2022

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Open.
Studio
# Objective: use the latest advances in graph learning methods to forecast industrial mutations
**Capture the underlying relationships between product classes in the Product Space**
<figure><img src="image_5.png" /><figcaption>Product Space on 4 digits (1604 products)</figcaption></figure>
We built the Product Space on 6 digits (5040 products)

<figure><img src="image_6.png" /></figure>
We consider the dynamic Product Space as a
discrete-time dynamic graph (DTDG)
consisting of a sequence of snapshots from
a dynamic graph sampled at regularly-
spaced times
<figure><img src="image_7.png" /><figcaption>We built snapshots of Product Spaces over 25 years for each country</figcaption></figure>
Predicting the **Dynamic Embedding**
**Trajectory** in Temporal Networks
<figure><img src="image_8.png" /></figure>

Li, J., Han, Z., Cheng, H., Su, J., Wang, P., Zhang, J., & Pan, L. (2019). *Predicting Path Failure In Time-Evolving Graphs* (arXiv:1905.03994). arXiv. http://arxiv.org/abs/1905.03994
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Architecture:

$$
\textbf{Graph Convolutional Network (GCN)} \\
+ \\
\textbf{Long Short Term Memory (LSTM)}
$$
# Experiments & Results

We use the Pytorch Geometric Temporal library

Source code: https://github.com/apachot/pytorch_geometric_temporal

<table><thead><tr><td></td><td>Dynamic structure</td><td>Temporal features</td><td>MSE</td></tr></thead><tbody><tr><td>Graph Convolutional Network</td><td>no</td><td>yes</td><td>0.045</td></tr><tr><td>Long Short Term Memory Relational Graph Convolutional Network</td><td>yes</td><td>yes</td><td>0.022</td></tr></tbody></table>
Conclusions & Perspectives

<figure><img src="image_10.png" /><figcaption>Growth Projections to 2030 (Annual Growth, %)</figcaption></figure>

* We can predict the evolution of the Product Space of a country using graph learning methods

* Our results must be compared with the growth models proposed by the complexity theory
Thank you !

Arnault Pachot

apachot@openstudio.fr

arnault.pachot@etu.uca.fr

https://www.linkedin.com/in/arnaultpachot/

https://github.com/apachot/pytorch geometric temporal