Where and when

teachers: Emma Perracchione⁽¹⁾ and Sabrina Guastavino⁽²⁾  
affiliation: ⁽¹⁾DISMA | Dipartimento di Scienze Matematiche of the Politecnico di Torino, ⁽²⁾DIMA | Dipartimento di Matematica of the Università di Genova   
date: June 12-16^th, 2023   
venue: Turin (Italy), DISMA | Dipartimento di Scienze Matematiche – Politecnico di Torino (Auletta Seminari DISMA)

Kernels for Machine learning: Applications to Solar Physics

This PhD course is carried out and supported by the project Physics-based AI for predicting extreme weather and space weather events (AIxtreme) funded by La Fondazione Compagnia di San Paolo and Fondazione CDP.

Course contents and program can be find below: In the machine learning framework, kernel-based models play a crucial role. The course will be devoted to presenting and studying, at first, kernels and associated native spaces. Moreover, some techniques of standard learning, as SVM, will be presented by using novel and recent tools, such as the variably scaled kernels. Such techniques can be applied in the context of astronomical imaging and the basics concerning the reconstruction problem of solar flares sampled by the telescope STIX, on board Solar Orbiter, will be provided. The data utilized in some test cases, provided by the ESA mission Solar Orbiter in collaboration with NASA, are publicly available. The second part of the course will be more computationally oriented and will mainly focus on machine learning techniques as neural networks for prediction problems and methods enhancing sparsity for the selection of most predictive features by focusing on their usage in the context of solar physics. More specifically, in order to extract the most relevant features, examples concerning the prediction of solar flares and iterative methods will be shown.

The schedule is below:

• Monday 12 June    
  10.00 am - 12.00 pm 
  2.00 pm - 4.00 pm
• Tuesday 13 June 
  2.00 pm - 4:00 pm
• Wednesday 14 June 
  10.00 am - 12:00 pm 
  2:00 pm - 4:00 pm
• Thursday 15 June    
  10.00 am - 12:00 pm 
  2:00 pm - 4:00 pm
• Friday 16 June 
  10.00 am - 12.00 pm 
  
  Depending on the students, classes might be given in Italian language and for reasonable and specific requests virtual classrooms could be used. The final examination consists of a brief report on some selected topics.

The program of the course can be summarized as follows:

1. Kernels for interpolation problems from sparse data: introduction to kernels and error analysis in the native spaces.

2. Variably Scaled Kernels (VSKs): study of the recent variably scaled kernels and error analysis in the so-generated native spaces.

3. Applications of kernel methods to inverse problems in solar physics.

4. Laboratory devoted to the implementation (mainly in Matlab language) of the techniques based on VSKs.

5. Machine learning for forecasting problems (classification and regression): introduction to neural networks.

6. Selection of most predictive features: studying methods that enhance sparsity as lasso and iterative methods.

7. Forecasting problems in solar physics: introduction to the problem of solar flare forecasting and its mathematical formulation.

8. Laboratory devoted to the implementation (in Matlab or Python languages) of the neural networks analyzed during the lecturers.

Thanks to all participants!

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