From public discussion, you may get the impression that there are no problems that could not be solved by means of artificial intelligence (AI). This is not actually true, however.

People’s conceptions of AI are easily biased towards creations of strong AI familiar from science fiction, which are capable of human decision-making and of imitating human thinking.

At present, we are far from that.

Instead, we have learned to use weak AI. In principle, such applications are trained to solve a single specific problem. For example, weak AI can be taught to recognise hand-written alphabets. For this purpose, it is exposed to a large set of images of hand-written alphabets and told which alphabet each image stands for. In connection to such training, the algorithm adjusts the weighting factors included in the AI application so that it can associate certain types of images with the corresponding alphabet.

**AI is an approximation of a mapping**

In mathematical terms, AI is essentially about a function from a domain to a codomain. Just like the function ƒ (*x*) = sin (*x*) maps all real numbers *x* for the range [−1,1]. In weak AI, these mappings are usually much more complex and not defined in any straightforward way. For this reason, AI must be considered an approximation of a true description.

For example, artificial neural network models consist of several composite mappings, so they may include millions of adjustable factors. In the late 1980s, it was shown that a mapping meeting certain preconditions can be approximated with this kind of a neural network. Because AI applications are taught with certain source data, their capability to generalise the outcome is strongly dependent on the source data. How extensive is it? How high quality is it? How many elements are there?

**Taking advantage of the benefits of modelling**

Collecting data in order to teach AI applications is essential. In many applications, the collection process is slow, time-consuming and expensive. From the perspective of large-scale use of even a weak AI, it would be worthwhile to find solutions to this problem. In certain settings, computational science and mathematical modelling offer us tools for solving this issue.

By means of mathematical models, we can simulate a phenomenon we wish to teach to an AI application.

In such a case, a computer can produce a large set of data, all parameters of which we know. For instance, we can first model the travel of light on a single leaf of a tree, then in a tree and a forest, and how light scatters outwards from there. Training AI to approximate the inverse mapping of this simulation, we can determine from an image some biophysical and biochemical parameters of the leaf. Drawing on this knowledge, we can simulate new training data based on already collected images.

Alternatively, inverse description can be used in explaining why an AI algorithm works the way it works. This may concern, for example, recognition of different tree species, the health of trees, or even skin cancer. Traditional mathematical modelling combined with AI research can provide new dimensions for many fields of science as well as for society. Although AI research is now fashionable, there is also reason to appreciate more traditional computational science, which encompasses themes ranging from mathematical modelling and simulation to scientific computing.

The spectral imaging laboratory of the JYU Faculty of Information Technology is doing research on these themes. Our research encompasses both mathematical modelling and development of AI methodology as well as endeavours to make use of the scattering of light for various applications. At present, things like those described above are studied at the University of Jyväskylä in projects funded by the Academy of Finland: Spectral Imaging of Complex Surface Tomographies (SICSURFIS) and Autonomous Tree Health Analyzer Based on Imaging UAV Spectrometry (ASPECT).

*Docent Ilkka Pölönen*

*The writer is the Principal Investigator of the SICSURFIS and ASPECT projects.*

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