When mathematics helps optimize experimental approaches

Today, machine learning has become an essential tool in applied mathematics for designing data processing methods capable of solving complex problems. Statistical models are trained on generated data to predict new cases. But a crucial question remains: what is the most relevant data to generate?

Because while the era of “big data” allows for the accumulation of information on a massive scale, generating data requires time, energy, and resources. This is particularly true in the field of cosmetic formulation, where the development of new products often requires numerous experimental trials.

It is within this context that Clara Guilhaumon’s thesis is situated, conducted in collaboration between the School of Industrial Biology (EBI) and ENSAM – Arts et Métiers. Her objective: to develop automatic and efficient methods for intelligently generating data, capable of selecting a small number of judiciously chosen experiments, but sufficient to train a reliable statistical model.

The approaches developed in this thesis are tested on several case studies:

• In mechanics, a field of expertise for Arts et Métiers,
• and in cosmetic formulation, EBI’s preferred area of ​​expertise.

In this last example, the goal was to design a new skincare cream with a specific texture, dependent on both the ingredients used (types and concentrations) and the manufacturing process parameters (temperature, mixing speed, etc.). Rather than conducting numerous time-consuming trials, the team applied the methods developed by Clara to select a small but optimal number of mixtures. From this limited data, a statistical model was trained, allowing for the accurate prediction of the ideal combination of ingredients and parameters to achieve the desired texture.

This new approach opens up promising perspectives in many fields. In cosmetics, it can facilitate the creation of personalized products and accelerate the development of new formulas. In healthcare, it could contribute to the development of tailored treatments that are more effective and better suited to each patient.

By placing applied mathematics at the heart of experimentation, Clara Guilhaumon’s work perfectly illustrates how interdisciplinary research can transform scientific practices — by making them more precise, faster, and more responsible.

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Your contacts: Clara Guilhaumon, clara.guilhaumon@ensam.eu; Marc Lavarde, Professor of Applied Mathematics, Head of the Galenic Research Area, m.lavarde@ebi-edu.com