Fundamentals of Geographical Information Systems
Geographic coordinates systems
Vector data model
Trajectories
Spatial Tessellations
Flows
Practice: Python packages for geospatial analysis (Shapely, GeoPandas, folium, scikit-mobility)
Digital spatial and mobility data
Mobile Phone Data
GPS data
Social media data
Other data (POIs, Road Networks, etc.)
Practice: reading and exploring spatial and mobility datasets in Python
Preprocessing mobility data
filtering compression
stop detection
trajectory segmentation
trajectory similarity and clustering
Practice: data preprocessing with scikit-mobility

Module 2: Mobility Patterns and Laws

individual mobility laws/patterns
collective mobility laws/patterns
Practice: analyze mobility data with Python

Module 3: Predictive and Generative Models

Prediction
Next-location prediction
Crowd flow prediction
Spatial interpolation
Generation
Trajectory generation
Flow generation
Practice: mobility prediction and generation in Python

Module 4: Applications

Urban segregation models
Routing and navigation apps
Traffic simulation with SUMO

Basic concepts and models: Continuos and discrete hypothesis space, inductive bias, linear and nearest neighbor models (learning algorithms and properties), regularization.

Neural Networks (NN) architectures and learning algorithms: Perceptron. Multi-layers feedforward models. Deep models. Randomized NN. Recurrent NN. Regularization.

Validation: model selection and model assessment.

Principles of learning processes: Elements of Statistical Learning Theory. Bias/variance analysis.

Support Vector Machines and Kernels-based models.

Unsupervised learning: vector quantization, self-organizing map (SOM).

Introduction to benchmarks and applications.

Introduction to advanced approaches (structured domains, learning on graphs).

– Introduce the concepts of minimization algorithms for a scalar functional (the loss function).
– Provide the necessary tools for practical course execution, such as Python, Tensorflow, and Pytorch.
– Cover dense neural networks and examples of their applications in physics.
– Explore convolutional neural networks and examples of their applications in physics.
– Discuss recurrent neural networks and examples of their applications in physics.
– Investigate graph neural networks: inductive bias and examples of their applications in physics.
– Examine attention mechanisms: transformers and examples of their applications in physics.
– Study generative neural networks and examples of their applications in physics.
– Provide an overview of differentiable programming.

The course encompasses these topics to provide students with a comprehensive understanding of machine learning algorithms in the context of physics applications.