Thousands of biogas digesters operate across rural farms and households in Bangladesh, yet their operational dynamics, efficiency, and methane production behavior remain largely unquantified. Although biogas is a promising renewable energy source for sustainable development and energy independence, most systems operate reactively due to the lack of real-time monitoring and predictive intelligence. Operational issues such as pressure buildup, gas leakage, digester imbalance, and suboptimal methane yield are often detected only after performance degradation occurs. This study proposes SmartBioGas-PIoT, a physics-informed, TinyML-enabled Edge AI framework for real-time monitoring and methane production rate prediction in anaerobic biogas digesters. The system continuously measures internal and external temperature and humidity, , and pressure, with data processed directly on an ESP32 microcontroller. Unlike conventional black-box approaches, the methane production rate is calibrated using ideal gas-based pressure–volume relationships to ensure thermodynamic consistency. Three regression models, including Linear Regression, Ridge Regression, and Random Forest Regressor, were evaluated, with the Random Forest Regressor achieving superior performance ( = 0.9824). The trained model was exported using MicroMLgen and deployed on-device, enabling low-latency, cloud-independent methane rate estimation. Cyclic time encoding was incorporated to capture diurnal and weekly patterns in biogas generation. By integrating thermodynamic modeling, embedded sensing, and on-device intelligence into a unified IoT architecture, the proposed system provides a scalable, cost-effective solution for intelligent biogas management in resource-constrained environments.