Lectures
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Course Introduction and Logistics
Overview of Scientific Machine Learning and Course Structure
Lecture Materials
Recommended Papers
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Data, Modeling, and Inference
Empirical Laws and Linear Regression
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Introduction to Supervised Learning
Linear Regression, Logistic Regression, Feature Engineering, Generalized Linear Models, Maximum Likelihood Estimation, Multiclass Classification
Recommended Readings
Lecture Materials
- Introduction to Supervised Learning Overview Lecture Slides - (see first 10 minutes)
- Linear Regression Introduction Notes - Hooke's Law
- Code: Linear Regression toy problem (Colab)
- Code: Introduction from Linear Regression to Deep Learning - with references
- Code Walkthrough Video: Introduction to Scikit-learn
- Introduction to Linear Regression
- Feature Engineering and Generalization
- Introduction to Logistic Regression - Coming Soon
- Why Ordinary Least Squares? Maximum Likelihood Estimation
Recommended Videos
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Introduction to Deep Learning
Nonlinear Predictors, Neural Networks, Activation Functions, Backpropagation, etc
Recommended Readings
Lecture Materials
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Time Series Analysis
Time series analysis, autoregression, recurrent neural networks, state-space models, probabilistic models, etc.
Suggested Motivation Videos
Lecture Materials
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Modeling the World with Differential Equations
ODEs, PDEs, Complexity and Uncertainty
Lecture Materials
- Pondering on the Nature of Complexity in Science and Machine Learning
- Everything is a Function
- Complex Systems and Differential Equations
- Introduction to Numerical Integration
- The story of the Lorenz System: Nonlinearity, Chaos, Uncertainty Quantification
- Introduction to Partial Differential Equations
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Symbolic Identification of Differential Equations from Data
Given data in space and time, how can we find its corresponding equation using sparse linear regression?
Recommended Readings
Recommended Videos
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Residual Minimization & Physics Informed Neural Networks
Including physical knowledge in a loss function
Recommended Readings
Recommended Videos
Lecture Materials