## 1 Introduction  
During surgical procedures, as patients undergo anesthesia, the administration of Remifentanil and Propofol stands as a cornerstone, actively shaping the patient's physiological responses. These pharmacologically distinct agents, an opioid analgesic and a hypnotic, contribute to achieving and maintaining an optimal level of anesthesia. However, beyond their primary hypnotic and analgesic roles, these drugs may exert side effects, potentially influencing the physiological response of the patient, specifically the mean arterial pressure (MAP) [1]. MAP serves as a vital indicator of perfusion and oxygen delivery to organs, making its accurate prediction during surgery imperative [2]. The challenge at hand is not only to comprehend the dynamics of how Remifentanil and Propofol influence MAP but also to devise an online predictive framework that balances the need for accuracy with computational efficiency. Artificial intelligence (AI) has revolutionized various aspects of the medical field, offering advanced solutions for diagnostics, treatment planning, and patient management [3; 4]. In the domain of AI applications in anesthesia, the complex interplay between drug administration and patient physiological responses has been a focal point of exploration [5]. Understanding this dynamic interaction is crucial for optimizing patient outcomes. There exists a relationship between the architectural design of neural network models and their predictive performance [6]. LSTM architecture selection for predicting physiological parameters has received notable attention [7] because of its proficiency in capturing temporal dependencies within the data [8; 9]. LSTM networks have been increasingly applied in the prediction of medical signals due to their ability to model time series data effectively. Particularly in the context of irregularly sampled medical time series, which is common in healthcare data [10], LSTMs demonstrate notable advantages. These networks adeptly handle intra-series irregularities (varying time intervals within a single data stream) and inter-series irregularities (different sampling rates across multiple data streams) [11; 12]. This capability is crucial for modeling complex medical signals, e.g., blood pressure, where data points might be unevenly spaced in time. Further, the integration of LSTMs with other neural network architectures, like Convolutional Neural Networks (CNNs), has shown promising results in the medical field. Specifically for anesthesia, using inputs like Propofol and Remifentanil to predict MAP, the ability of LSTM to capture temporal dependencies and handle missing or irregular data points makes it a suitable choice. The ability of LSTM to process time-dependent data and handle variations in data sampling rates are key reasons for their suitability in estimating MAP under anesthesia. The choice of the best architecture for LSTM models has often been driven either by tests involving multiple architectures, or by the background expertise of researchers [13; 14]. The following question arises: is the selected LSTM architecture truly the optimal choice for a given AI application, or is there an optimal criterion that demands consideration, e.g., the computational time? We recognize the need to build more optimal architectures for deep learning models, with enhanced accuracy and computational efficiency, since we aim to obtain an online MAP estimation solution. In this context, our paper addresses this dual imperative by introducing three distinct selection approaches of the LSTM architecture. The first method involves a population-based architecture, considering 70 patients under anesthesia. The second method adopts a patient-specific strategy, building an LSTM architecture uniquely for each patient.