Russian Scientists Reconstruct Dynamics of Brain Neuron Model Using Neural Network
Researchers from HSE University in Nizhny Novgorod have shown that a neural network can reconstruct the dynamics of a brain neuron model using just a single set of measurements, such as recordings of its electrical activity. The developed neural network was trained to reconstruct the system's full dynamics and predict its behaviour under changing conditions. This method enables the investigation of complex biological processes, even when not all necessary measurements are available. The study has been published in Chaos, Solitons & Fractals.
Neurons are cells that enable the brain to process information and transmit signals. They communicate through electrical impulses, which either activate neighbouring neurons or slow them down. Each neuron has a membrane that allows charged particles, known as ions, to pass through channels in the membrane, generating electrical impulses.
Mathematical models are used to study the function of neurons. These models are often based on the Hodgkin-Huxley approach, which allows for the construction of relatively simple models but requires a large number of parameters and calculations. To predict a neuron's behaviour, several parameters and characteristics are typically measured, including membrane voltage, ion currents, and the state of the cell channels. Researchers from HSE University and the Saratov Branch of the Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences have demonstrated the possibility of considering changes in a single control parameter—the neuron's membrane electrical potential—and using a neural network to reconstruct the missing data.
The proposed method consisted of two steps. First, changes in a neuron's potential over time were analysed. This data was then fed into a neural network—a variational autoencoder—that identified key patterns, discarded irrelevant information, and generated a set of characteristics describing the neuron's state. Second, a different type of neural network—neural network mapping—used these characteristics to predict the neuron's future behaviour. The neural network effectively took on the functions of a Hodgkin-Huxley model, but instead of relying on complex equations, it was trained on the data.
'With the advancement of mathematical and computational methods, traditional approaches are being revisited, which not only helps improve them but can also lead to new discoveries. Models reconstructed from data are typically based on low-order polynomial equations, such as the 4th or 5th order. These models have limited nonlinearity, meaning they cannot describe highly complex dependencies without increasing the error,' explains Pavel Kuptsov, Leading Research Fellow at the Faculty of Informatics, Mathematics, and Computer Science of HSE University in Nizhny Novgorod. 'The new method uses neural networks in place of polynomials. Their nonlinearity is governed by sigmoids, smooth functions ranging from 0 to 1, which correspond to polynomial equations (Taylor series) of infinite order. This makes the modelling process more flexible and accurate.’
Typically, a complete set of parameters is required to simulate a complex system, but obtaining this in real-world conditions can be challenging. In experiments, especially in biology and medicine, data is often incomplete or noisy. The scientists demonstrated by their approach that using a neural network makes it possible to reconstruct missing values and predict the system's behaviour, even with a limited amount of data.
'We take just one row of data, a single example of behaviour, train a model on it, and incorporate a control parameter into it. Imagine it as a rotating switch that can be turned to observe different behaviours. After training, if we start adjusting the switch—ie, changing this parameter—we will observe that the model reproduces various types of behaviours that are characteristic of the original system,' explains Pavel Kuptsov.
During the simulation, the neural network not only replicated the system modes it was trained on but also identified new ones. One of these involves the transition from a series of frequent pulses to single bursts. Such transitions occur when the parameters change, yet the neural network detected them independently, without having seen such examples in the data it was trained on. This means that the neural network does not just memorise examples; it actually recognises hidden patterns.
'It is important that the neural network can identify new patterns in the data,’ says Natalya Stankevich, Leading Research Fellow at the Faculty of Informatics, Mathematics, and Computer Science of HSE University in Nizhny Novgorod. 'It identifies connections that are not explicitly represented in the training sample and draws conclusions about the system's behaviour under new conditions.'
The neural network is currently operating on computer-generated data. In the future, the researchers plan to apply it to real experimental data. This opens up opportunities for studying complex dynamic processes where it is impossible to anticipate all potential scenarios in advance.
The study was carried out as part of HSE University's Mirror Laboratories project and supported by a grant from the Russian Science Foundation.
See also:
‘The Peak of Stupidity’ and ‘The Valley of Despair’: HSE Economists Propose an Explanation for the Dunning–Kruger Effect
The Dunning–Kruger effect, which describes a sharp surge in self-confidence among beginners followed by an equally rapid decline as they gain experience, can be explained by the nature of the learning process and the acquisition of new knowledge. This conclusion was reached by Andrey Vorchik of the HSE Faculty of Economic Sciences together with independent researcher Murat Mamyshev. They developed a mathematical model of learning and demonstrated how subjective confidence is formed and changes as knowledge accumulates, as well as how teachers can reduce the ‘valley of despair’ experienced by learners.
Toffee and Risk: Scientists Discover Why People Who Crave Sweets Make More Impulsive Choices
Having a sweet tooth may be linked not only to eating habits but also to the way people make decisions. Researchers at HSE University have found that people with a preference for sweet foods tend to behave more impulsively—not because they want immediate rewards, but because they are less willing to tolerate uncertainty. These findings may help improve treatments for addiction. The study findings have been published in Frontiers in Psychology.
Physicists Find a Way to Model Ion Parameters in Plasma in Seconds
Researchers from HSE University and the Moscow Institute of Physics and Technology (MIPT) have developed a set of simple analytical methods for calculating the properties of heavy ions in helium under the influence of a strong electric field. The new approach speeds up calculations of ion mobility and ion–molecule reaction rates by thousands of times while maintaining sufficient accuracy for plasma jet modelling. The findings have been published in the journal Physica Scripta.
Two Years of Growth or Decline: How to Choose an Investment Strategy
Economists from HSE University, together with colleagues from international universities, have analysed stock market movements over almost a century and proposed an investment strategy that could have delivered returns nearly twice as high as the market average. Their research suggests following a momentum strategy during periods of sustained market growth and switching to a value strategy after prolonged market declines. The study has been published in the Journal of Banking and Finance.
Researchers Reveal Link Between Attention and Communication Difficulties in Autism
Researchers at HSE University have examined how communication difficulties in children with autism are related to brain function. The findings show that not only language networks but also attention networks play an important role. The weaker the connections involved in maintaining focus and switching attention, the more pronounced communication difficulties were. The study has been published in European Child & Adolescent Psychiatry.
Scientists Discover Why Some People Wore Masks During COVID-19 While Others Did Not
Why do some people voluntarily follow new rules while others ignore them? Researchers at HSE University have found that the answer lies not so much in people's willingness to cooperate, as previously believed, but in their ability to empathise with others. Empathy proved to be the strongest predictor of whether people chose to wear face masks voluntarily during the COVID-19 pandemic. The findings have been published in Frontiers.
'Physics Is What the World Is Literally Built On'
Physicist Nina Dzhanayeva, recipient of a Vladimir Potanin Foundation scholarship, focuses her research on nanophotonics. In this interview for the HSE Young Scientists project, she discusses nanowells, scientific intuition, and how physics can help in making frangipane cream puffs.
Physicists at HSE University and FIAN Discover Way to 'Photograph' Sound for Testing Materials Used in 6G Communications
Researchers at HSE University, in collaboration with colleagues from the Lebedev Physical Institute of the Russian Academy of Sciences (FIAN), have developed a method for rapidly determining how firmly a film is bonded to a substrate. This is important for the creation of ultrahigh-frequency acoustic filters, which are key components of next-generation 5G and 6G communications. For the first time, researchers have succeeded in measuring the lateral rigidity of the bond between a two-dimensional material film and a substrate in this way. The study results have been published in Applied Physics Letters.
Scientists Create Open Dataset for Studying Concentration
A team of Russian researchers, including scientists from HSE University–St Petersburg, has developed the first open multimodal dataset containing recordings of brain activity, heart function, and video observations to help researchers understand what happens in the human brain during deep concentration. In the future, the dataset could accelerate the development of neural interfaces, rehabilitation technologies, and AI systems. The article has been published in Scientific Data.
Scientists Propose Method for More Efficient Resource Use in Machine Learning
An international group of researchers, including mathematicians from the AI and Digital Science Institute at the HSE Faculty of Computer Science, has provided a theoretical justification for a simple and computationally efficient method of estimating uncertainty in Stochastic Gradient Descent (SGD). The paper has been published on the scientific preprint server arXiv.org and presented at AISTATS 2026.