markdown with math formulas

[LessGoudarzi]

Sure, I can provide a numerical example using best estimates of the parameters from the web. Please note that these estimates may vary depending on the specific use case and location.

Let's consider a scenario where we want to estimate the energy consumption of a deep learning model deployed on a cloud-based platform.

Model-Specific Energy Consumption

• Model complexity (M): 100 million parameters (e.g., a large language model like BERT)
• Deployment environment (D): Cloud-based (e.g., AWS, Google Cloud)
• Frequency of inference requests (F): 100 requests per second
• Volume of inference requests (V): 10,000 requests per hour
• Hardware efficiency (H): 10W per unit (e.g., using NVIDIA V100 GPUs)

Using the equation:

$$ [E = \alpha \times M \times D \times F \times V \times H] $$

where (\alpha) is a constant that represents the energy consumption per unit of model complexity, deployment environment, frequency, volume, and hardware efficiency.

$$ Assuming (\alpha = 0.01) $$

(a rough estimate based on various studies), we get:

$$ [E = 0.01 \times 100,000,000 \times 1 \times 100 \times 10,000 \times 10 = 100,000 \text{ Wh}] $$

Data Center Energy Consumption

• Power usage effectiveness (PUE) ratio (P): 1.5 (a typical value for cloud data centers)
• Geographical location of data center (G): 1 (assuming a data center in the US with average energy efficiency)

Using the equation:

$$ [E_{DC} = P \times G \times E] $$

we get:

$$ [E_{DC} = 1.5 \times 1 \times 100,000 = 150,000 \text{ Wh}] $$

Scalability Analysis

• Scalability factor (S): 2 (assuming a linear scaling of energy consumption with the number of inference requests)
• Network overheads (N): 10% (assuming a 10% overhead due to data transmission and networking)

Using the equation:

$$ [S = \beta \times E \times N] $$

where

$$ (\beta) $$

is a constant that represents the scalability factor, we get:

$$ [S = 2 \times 100,000 \times 0.1 = 20,000 \text{ Wh}] $$

Total Energy Consumption

The total energy consumption of the deep learning model can be estimated by adding the energy consumption of the model, data center, and scalability:

$$ [E_{total} = E + E_{DC} + S = 100,000 + 150,000 + 20,000 = 270,000 \text{ Wh}] $$

This translates to approximately 270 kWh of energy consumption per hour.

Carbon Footprint

Using the average carbon intensity of the US grid (approximately 0.45 kg CO2e/kWh), we can estimate the carbon footprint of the deep learning model:

$$ [CF = E_{total} \times CI = 270,000 \text{ Wh} \times 0.45 \text{ kg CO2e/kWh} \approx 121.5 \text{ kg CO2e/h}] $$

This is equivalent to approximately 121.5 kg CO2e per hour.

Please note that these estimates are rough and based on various assumptions. The actual energy consumption and carbon footprint of the deep learning model may vary depending on several factors, including the specific hardware, software, and deployment environment used.