• Introduction to AI and machine learning in the Energy Sector
• Data pre-processing and visualization
• Supervised learning
  • Linear and regularized regression models
  • Decision Trees, bagging and boosting
  • Neural Networks and back-propagation
  • Deep Learning
• Unsupervised learning
  • Clustering
  • Dimensionality reduction
• Reinforcement Learning

Reference material

• Class notes
• Trevor Hastie - An Introduction to Statistical Learning: with applications in Python. Available at https://www.statlearning.com/
• Aurélien Géron - Hands on machine learning with scikit-learn and pyTorch. Available at https://github.com/ageron/handson-ml3
• Andrew Barto and Richard S. Sutton - Reinforcement Learning: An Introduction (MIT Press, Cambridge)
• Anoop Krishnan, Hariprasad Kodamana and Ravinder Bhattoo - Machine Learning for Materials Discovery (Springer)
• Christopher M. Bishop - Pattern Recognition and Machine Learning (Springer)

Energy

• Powers everything from molecular interactions to large scale infrastructure on Earth.
• Transitioning to sustainable energy systems is required for persistence of human life and environment as we know it.

Innovation and energy that fuelled it underpins economic growth

Current Issues

Energy transition

Energy transition

• Structural shift from fossil-based (coal, oil, gas) to low or zero-carbon sources (renewables, nuclear, potentially hydrogen)
• More than swapping sources: involves change in infrastructure, technology, policy, markets and consumer behavior

Opportunities and Challenges

Vision

• System level: more electric, distributed resources, variable generation
• Operational level: more resilient, efficient solutions with righ infrastructure
• Pathway 1-CCS: carbon capture and storage for decarbonization
• Pathway 2-RE: Renewables as clean energy

The pillars of transition

The classes of problems

• Optimization problems
• Control problems
• Simulation problems
• Decision problems
• Uncertainty quantification problems
• Learning problems
• Multiscale problems

How AI could offer solutions

AI Models: Understanding, Prediction and Creation

• Traditional AI tasks - understanding or discriminating between existing data points (e. g., classification and regression)
• AI tasks for prediction - forecasting future data points (e. g., time series prediction, demand forecasting)
• AI tasks for creation - Gen AI (e. g., new process routes, new materials, reducing boilerplate tasks)

Data in Energy Systems

• Types of energy data:
• Time series data (load, generation)
• Spatial data (wind farms, grids)
• Graph-based (power networks)
• Issues:
• Missing data
• Measurement noise
• Non-stationarity
• Physical meaning of data

What makes energy AI different from Generic ML

• Physical constraints (conservation, limits, non-negativity)
• Safety-critical decisions (small error ->cascade failures)
• Long time horizons (e.g. battery degradation, error compounding)
• Policy & economics coupling (multiphysics, predictions change consumer behavior)
• Interpretability requirements (Regulators need reasons for decisions)

Physical models vs Data-driven models

Errors, Uncertainty and Risk

• Mean error vs. worst-case error
• Cost of errors
• Uncertainity matters more than accuracy
• Predictions can be deterministic vs. probabilistic
• Energy decisions are risk-based and not error-based.

Anatomy of an ML model

• Inputs (features): Measured (derived), e.g, wind speed, irradiance, occupancy in a building, temperature, current
• Raw features may have a lot of redundancy
• Outputs (targets): The quantity the model predicts, e.g, Power output, demand, system state, remaining life of assets. Derive decisions based on output.
• Model structure (hypothesis space): Mapping from input to output. E.g., Linear regression-weighted sum, NN-nonlinear transformations.
• Parameters: What the model learns. E.g., Weigts, thresholds
• Loss function: Measure of prediction error. E.g., mean squared error, cost weighted loss
• Training: Process of adjusting the parameters so the model becomes accurate
• Inference: Using the model on unseen data
• Generalization: Performance on unseen conditions. E.g., Heatwave conditions not seen in data, New grid topology.
• Uncertainty & Confidence: Quantifying how sure the model is. E.g., forecast bands, risk-awareness

Python language as a thinking tool

• Experiment notebook
• Analysis tool
• Simulation tool

What is learning from data?

• Model estimation methods
• Bias and variance tradeoff
• Model accuracy

What is a model?

• Goal: Predict energy consumption for building
• Inputs: Sq. footage, occupants, appliances, temperature, day of week
• Outputs: Energy consumption
• Model: $Y= f(\mathbf{X}) + \epsilon$, where $\mathbf{X} = (X_1, X_2, \cdots, X_p)$
• $f$ is fixed by unknown. $\epsilon$ is random error, independent of X, mean zero.
• $f$ is systematic information that X provides about $Y$

Simpler example

Estimating f

• We may estimate f from given data as $\hat{f}$ and so $$ \hat{Y}=\hat{f}(\mathbf{X})$$
• $\hat{f}$ is an estimate of $f$, $\hat{Y}$ is resulting prediction of $Y$
• Hence the accuracy of $\hat{Y}$ as a prediction for $Y$ depends on:
  • reducible error
  • irreducible error
• Reducible: reduced by making $\hat{f}$ a perfect estimate of $f$
• Irreducible: Even if we get $\hat{Y}=f(\mathbf{X})$, there will be some error because $Y= f(\mathbf{X}) +$ $\epsilon$
• $\epsilon$ is either unmeasured variables or unmeasureable variation.

Prediction

• Consider an estimate $\hat{f}$ and predictors $\mathbf{X}$, yielding $\hat{Y}=\hat{f}(\mathbf{X})$
• Assume, $\hat{f}$ and $\mathbf{X}$ are fixed, and $\epsilon$ is random wit expectation 0.

Statistical Inference or interpretation

• Questions: Which predictors are associated with the response? Which are important?
• Relationship between the predictors? Positive or negative association?
• Can relationship between $Y$ and each feature be adequately summarize using linear functions? When is linear not adequate?
• Which factor contributes the largest to building energy use?: How much more energy will be consumed if I increase occupancy by 10%?
• Linear models are more interpretable.

Estimating $f$: Parametric forms

• Make an assumption on the mathematical form. E.g. $$ f(X) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_p X_p $$
• Above assumes a linear function with parameters $\beta_0, \beta_1, \beta_2, \cdots, \beta_p$
• Use training data to fit/train the model such that $$Y \approx \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_p X_p$$
• The problem of estimating $f$ simplifies to estimating the parameters $\beta_0, \beta_1, \beta_2, \cdots, \beta_p$
• Disadvantage: The model may be far from the true form of $f$
• Then we could use flexible models: but causes overfitting.

Linear fit

• Model will usually not match the true unknown form of $f$.
• A more flexible model-more parameters-leads to over fitting

Non-parametric forms

• Seek an estimate of $f$ that gets as close to the data points as possible without being too rough or wiggly
• No assumption about the form of $f$
• A very large number of observations needed
• Fitting vs overfitting:

Smooth spline fit

Rough spline fit

Accuracy vs Interpretability

• Linear regression is inflexible, whereas splines are flexible. Then why use a linear model?
• Better interpretability. it will be quite easy to understand the relationship between $Y$ and $X_1 , X_2 , \cdots X_p$
• Sometimes the less flexible model is also better for accuracy (potential for overfitting in higher flexibility models).

Model accuracy

• How do we measure performance of a learning method?
• Regression:mean-squared error $$ MSE = \frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{f}(x_i))^2$$
• Common loss functions include mean squared error, mean absolute error, and root mean squared error

Sometimes you need more than MSE

Test MSE vs Train MSE

• we are interested in the accuracy of the pre- MSE dictions that we obtain when we apply our method to previously unseen test data
• Examples: Stock profile, patient data
• Given a model trained on $\{ (x_1,y_1), (x_2,y_2), \cdots, (x_n,y_n) \}$, i.e. $\hat{f}(x_1), \hat{f}(x_2), \cdots, \hat{f}(x_n)$.
• We want to know how well $\hat{f}(x_0)$ predicts $y_0$.
• Ave$(y_0 - \hat{f}(x_0))^2$ for all such $(x_0,y_0)$.
• What if we don't have test data? Can we rely on train MSE?
• But training MSE could be quite small while test MSE is large.

Test vs Train MSE

• Grey lines:train MSE, red lines: test MSE. Blue and green lines: spline curves with increasing degrees of freedom.
• The horizontal dashed line indicates Var($\epsilon$), the irreducible error, which corresponds to the lowest achievable test MSE among all possible methods. Hence, the smoothing spline repre- sented by the blue curve is close to optimal.
• monotone decrease in training MSE vs. U-shape in test MSE.

Bias-variance tradeoff

• The U-shape in test MSE: two competing properties.
• $E(y_0 - \hat{f}(x_0))^2 = \text{Var}(\hat{f}(x_0)) + \left[\text{Bias}(\hat{f}(x_0))\right]^2 + \text{Var}(\epsilon)$
• Variance: amount by which $\hat{f}$ would change if we changed the training data.
• Different training data, different $\hat{f}$.
• Linear fit has less variance.
• Bias: Error due to simplification. Linear regression has large bias.
• High flexibility - high variance, low bias.
• Low flexibility - low variance, high bias.

More examples

More examples

Data loading demo

Supervised vs. Unsupervised learning

• Unsupervised: given observations $x_1, x_2, \cdots, x_n$, find if data falls into groups
• Example: [wind speed, direction, power output, rotor speed, blade pitch angle, nacelle temperature, vibration indicators]
• Labels could be: [normal op., wake loss, icing, curtailment, incipient fault]
• Existense of semi supervised learning.

Model accuracy in classification

• Suppose we seek to estimate $f$ on $\{(x_1,y_1), (x_2,y_2), \cdots, (x_n,y_n)\}, where $y_1, \cdots, y_n $ are qualitative.
• Training error rate: mistakes made: $$ \frac{1}{n}\sum_{i=1}^{n}I(y_i \neq \hat{y}_i).$$
• Test error rate: Ave $(I(y_0 \neq \hat{y}_0))$ for all $(x_0,y_0)$.

Regression vs. classification

Classifier Accuracy