A new study by researchers from Tel Aviv University’s School of Chemistry presents an innovative approach to controlling random processes using an advanced mechanism known as adaptive resetting. According to the researchers, the method is expected to affect a wide range of fields, from computational algorithms and information searches to molecular simulations and the study of complex biological systems.
The study was conducted by doctoral students Tommer D. Keidar and Ofir Blumer under the supervision of Prof. Barak Hirshberg and Prof. Shlomi Reuveni of Tel Aviv University’s School of Chemistry. It was published in the journal Nature Communications.
Illustration explaining the study
(Illustration: Tel Aviv University)
The researchers offered an example from nature: Imagine a bee searching for nectar. The bee leaves the hive, its starting point, and moves in search of a flower, its target. Because the direction and location of the flower are not known in advance, the bee will choose a different path each time it leaves the hive, and the time it takes to reach the flower will therefore be random. Now imagine that, from time to time, the bee “resets” its movement by returning home. Such a mechanism is called random resetting.
For about a decade, scientists have known that many search processes can be accelerated through random resetting, or “returning home.” Until now, however, they assumed that the resetting process and the search process were independent of each other. This assumption made the mathematical analysis of the problem much easier, because equations that take into account the possibility that the bee can adapt its resetting strategy to environmental conditions were too difficult to solve. On the other hand, it is clear that if the bee is close enough to the flower to smell or see it, it will not want to return home before visiting the flower.
In the new study, researchers at Tel Aviv University’s School of Chemistry managed to overcome precisely this difficulty. They developed a method to predict how adaptive resetting processes will affect the bee’s movement. The method is highly general and can be applied to any random process, such as chemical reactions, changes in protein structure, algorithms for managing queuing systems and even learning processes in neural networks.
Prof. Barak Hirshberg Photo: Tel Aviv UniversityAccording to the researchers, the breakthrough has broad implications for statistical physics and computational chemistry, as it makes it possible to optimize search, calculation and simulation processes more accurately and efficiently. The study’s central importance lies in its proposal of a general way to predict and control the behavior of complex systems outside equilibrium — that is, changing and dynamic systems, a basic problem in modern science — while dramatically reducing the need for numerous costly computational runs.
The research team explains that “random resetting” is a mechanism that stops a given process and restarts it from a defined point. In recent years, this method has been found to significantly improve search and target-reaching processes, but until now it had been limited to cases in which resetting occurs independently of the system’s state. The new study breaks through that limitation and presents a general framework in which the resetting rate is adapted in real time to the state of the process and its history.
According to the researchers, the main innovation in the study is the ability to predict the system’s behavior under random resetting by analyzing only the dynamics without resetting, using a “reweighting” method. This approach makes it possible to calculate important measures such as the average time needed to reach a target, its distribution and steady states, without performing many complex simulations for each scenario separately.
Prof. Shlomi Reuveni Photo: Tel Aviv UniversityThe researchers demonstrated how the method can be applied to improve “smart” search strategies, for example when a search agent, such as an animal or an algorithm, changes its behavior according to its proximity to the target. Using the method, it is now possible to easily calculate how adapting the resetting rate to environmental information will affect search time — a necessary step toward designing better search strategies. In addition, the study showed the possibility of designing adaptive steady states that are not in full equilibrium in physical systems, an achievement that was not possible using previous resetting methods.
Beyond that, the researchers integrated machine learning into the model and showed that a neural network can be trained to automatically learn the optimal resetting strategy for a given task. This application led to a significant acceleration of molecular dynamics simulations, including complex processes such as protein folding, a field of great importance in medicine and biotechnology.
According to the researchers, the new approach is expected to open broad research and applied possibilities in statistical physics and computational chemistry, and to provide an efficient tool for designing complex processes in systems that are not in equilibrium.