Mathematical Modeling and Physics Informed Neural Network approaches for studying the environmental impact of data centers on a county level

Loudoun county in the state of Virginia in the United States is the world’s data center hub, with over 70% of global internet traffic flowing through the county. Rapid expansion of the internet and AI are accelerating data center growth, energy and water use, and emissions, posing a challenge to the UN Sustainable Development Goal (SDG) of net zero emissions by 2050. While estimates of global emissions from data centers exist, this would be the first study to estimate the direct and indirect environmental impact of data centers at the county level. Our study dynamically models the relationship between data center growth, population growth, and increased CO2 emissions using a system of coupled ordinary differential equations. The mathematical model thus accounts for the broader implications of data center concentration, such as its role in stimulating further infrastructure and land development, and assesses the impact on human mortality. Physics Informed Neural Networks (PINNs) are used with input from real-time data in Loudoun County to quantify parameters. Findings identify key causes and impacts of emissions related to data center growth at a local level, and define quantitatively the problem that sustainable energy solutions must address.