Advanced Weather Model Computing Development Act This bill requires the Department of Energy (DOE) and the National Oceanic and Atmospheric Administration (NOAA) to carry out research on advancing weather and climate modeling and prediction. DOE and NOAA must jointly carry out research on using artificial intelligence and high-performance computing for climate modeling and weather prediction. Research activities may include (1) developing new methods for modeling and simulation, machine learning, and predictive data analysis; and (2) facilitating data sharing between federal agencies, institutions of higher education, and other organizations. Additionally, NOAA must carry out an initiative to conduct proof-of-concept scenarios by comparing forecasts generated by advanced forecasting models with those generated by current models. As part of the initiative, NOAA may share innovations in the modeling system and applications through community-based activities and leverage climate and weather data and efforts of other federal agencies. NOAA must collaborate with DOE on the initiative. The research required by the bill must meet security and integrity requirements that apply to certain research activities of the National Science Foundation.