In an ideal medical environment, real-time coagulation monitoring can enable early detection and prompt remediation of risks. However, traditional Thromboelastography (TEG), a widely employed diagnostic modality, can only provide such outputs after nearly 1 hour of measurement. The delay might lead to elevated mortality rates. These issues clearly point out one of the key challenges for medical AI development: Making reasonable predictions based on very small data sets and accounting for variation between different patient populations, a task where conventional deep learning methods typically perform poorly. We present Physiological State Reconstruction (PSR), a new algorithm specifically designed to take advantage of dynamic changes between individuals and to maximize useful information produced by small amounts of clinical data through mapping to reliable predictions and diagnosis. We develop MDFE to facilitate integration of varied temporal signals using multi-domain learning, and jointly learn high-level temporal interactions together with attentions via HLA; furthermore, the parameterized DAM we designed maintains the stability of the computed vital signs. PSR evaluates with 4 TEG-specialized data sets and establishes remarkable performance -- predictions of R^2 > 0.98 for coagulation traits and error reduction around half compared to the state-of-the-art methods, and halving the inferencing time too. Drift-aware learning suggests a new future, with potential uses well beyond thrombophilia discovery towards medical AI applications with data scarcity.