# Time Scale Control Using Dynamic GMDH Neural Network Forecasting Based on Real Measurement Data
## 1 Introduction  
In the rapidly developing world of technology, the adaptability and flexibility of systems become crucial to achieving optimal efficiency and effectiveness. Some of the fundamental aspects of system control are managing the pace and continuity of operation, which are mainly responsible for time scales steering. Traditional methods of controlling time scales are often based on predefined rules or simple feedback loops. However, in complex and unpredictable environments, these methods may prove to be insufficient. Time scale control is required to ensure precise synchronization of the atomic clock implementing this scale with the UTC coordinated universal time [1]. National UTC(k) time scales are the basis for determining the official time in a given country, and are implemented by the leading National Metrology Institutes (NMIs). National NMIs strive to ensure the best possible stability and accuracy of their UTC(k). For this purpose, a direct comparison of a given UTC(k) with the global UTC scale, determined by the International Bureau of Weights and Measures, BIPM (in French, Bureau International des Poids et Mesures) is required [2, 3, 4]. This is mainly related to the need for the NMI to have a frequency that has high accuracy and stability, and also the possibility of its precise synchronization. This, in turn, very often is the basis for the safety and quality of many systems and for conducting basic scientific research. Currently, very important and advanced work is being carried out on the future definition of a second, according to the SI system, and on the revision of the definition of the international coordinated universal time, UTC. Every month and every week, for an individual UTC(k), the BIPM determines the UTC-UTC(k) and UTC-UTC(k) differences, respectively. The UTC-UTC(k) differences define the divergence of national time scales in relation to the UTC, while the UTC-UTC(k)differences define the divergence in relation to the UTC Rapid scale [5]. The UTC-UTC(k) differences for the previous month are published in the \"Circular T\" bulletin on MJD (Modified Julian Date) days ending with 4 and 9 (with a 5-day interval), most often in the second decade of the following month, while the UTC-UTC(k) differences for the previous week are published every Wednesday at 7:00 p.m. on the BIPM FTP server. Delays in the publication of the UTC-UTC(k) and UTC-UTC(k) differences by the BIPM cause difficulties in maintaining the highest possible level of compliance of the UTC(k) with the UTC. The main factor that influences this situation is the time needed to collect, properly prepare, and verify the measurement data from local and remote comparisons of over 700 atomic clocks [6], sent to the BIPM by the NMI, Designated Institutes, and other laboratories that are responsible for the implementation of local UTC(k) time scales, as well as the high complexity and time-consuming process of calculating the UTC scale by the BIPM [1,2]. In view of the problem of the delay in the publication of the differences determined by the BIPM, the control and determination of national UTC(k) time scales are based, in most cases, on forecasting methods (time or frequency scale). Statistical methods are used for this purpose, namely linear regression [7], Allan deviations [8], a Kalman filter [9], or stochastic differential equations [10]. In many cases, these methods are often combined with a heuristic decision-making process [7,11,12]. The availability of a local primary or secondary frequency standard (PFS or SFS) provided by the NMI, i.e., a caesium fountain, rubidium fountain, or optical clock [11], only allows for changing the time horizon of forecasts, or it may be more important in the case of a period of unavailability of PFS/SFS signals [6,11,12]. Forecasting has a significant impact on ensuring the greatest possible compliance of the UTC(k) with the UTC.