Using mathematics to understand how the brain works

By Johanne Høie Kolås og Jan-Eirik Welle Skaar

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Jan-Eirik Welle Skaar

Data and mathematics can help us analyze and simulate how networks of braincells work. This is the topic of Jan-Eirik Welle Skaar’s doctoral dissertation at NMBU.

In his research, Welle Skaar explores the use of data-driven and mathematical approximation methods to analyze and simulate neuronal networks. An approximation method is a technique used to find a solution to a problem that is too complex to solve exactly. Instead of finding the exact solution, you find one that is close enough to be useful.

“These methods are useful when working with large datasets or complex systems, such as neuronal networks, because they provide insights and results without using too much time and resources, says Welle Skaar.

Comparing data models with data from real brains

We know how neurons communicate, and we can simulate this by using biophysics-based models. In neuroscience, we use computational models to investigate the inner workings of the brain. They can help us understand how disease affects the brain and identify possible interventions and treatments.

“Computational models act as hypotheses, which can be compared to data from real brains. If there are mismatches between the computational model and the experimental data, the model can be updated and improved”, says Welle Skaar.

The networks that are formed by neurons in the brain are highly complex. They can be expensive to simulate, and they can be difficult to analyze.

“An important problem in constructing computational models is learning how to adjust the model parameters so that the networks behave similarly to real brains. This requires running large numbers of simulations to explore how the model behaves, says Welle Skaar.

In his doctoral work, he investigates how we can use data-driven machine learning methods to analyze neuronal networks and how we can use approximation methods to make the simulations faster.

“This is important for making realistic computer models and for simulating larger networks. My research shows how we can use machine learning to connect network behavior to model parameters, and develops approximation methods to quickly explore model behavior and more efficient simulations”, says Welle Skaar.

Jan-Eirik Welle Skaar will defend his PhD thesis "Approximation methods for analysis and simulation in computational neuroscience" on 13 May 2025. Read more about the event here.

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