Programme
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Short Course
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The Short Course will take place on Sunday 13th July 2025 (from 10.00am until 4.30pm) prior to the main IWSM conference. It must be added to your conference registration (for an additional fee).

Overview

Title. Physics-Informed Statistical Learning for Spatial and Functional Data

Abstract. This course offers an introduction to a family of physics-informed statistical learning methods designed for spatial and functional data. These models build upon nonparametric and semiparametric regression frameworks with roughness penalties. The penalties incorporate differential operators—ranging from simple second derivatives to more complex Partial Differential Equations—encoding the physics of the underlying phenomena, and complying with the geometry of the domain over which the data are observed. The methods can handle spatial and spatio-temporal data, as well as functional data, observed over multidimensional domains that can have complex shapes, such us non-convex planar regions, curved surfaces, irregular volumes, and linear networks. Moreover, the use of unstructured mesh discretization endows the methods with high flexibility, enabling the capture of highly localized signals, strong anisotropies, and non-stationary patterns. 

The course will explore these methods through real-world applications in environmental and life sciences, demonstrating their effectiveness in modeling intricate spatial and functional data structures. Practical lab sessions will utilize the R package fdaPDE.

Lecturers

Program Details

This course offers an introduction to a family of physics-informed statistical learning methods designed for spatial and functional data. These models build upon nonparametric and semiparametric regression frameworks with roughness penalties. The penalties incorporate differential operators—ranging from simple second derivatives to more complex Partial Differential Equations—encoding the physics of the underlying phenomena and complying with the geometry of the domain over which the data are observed.

A key strength of these methods is their adaptability to diverse data settings, including data observed over:

  • Planar domains, possibly with irregular boundaries (e.g., data scattered over land regions or water bodies with complex shorelines and islands);
  • Curved surfaces (e.g., global climate data, data observed over spatial regions with complex orography, biological signals mapped onto the surface of anatomical structures such as the brain);
  • Volumes, possibly featuring an irregular shape (e.g., atmospheric data, data collected in 3D land regions or water bodies, biological signals mapped onto the volume of anatomical structures such as the brain);
  • Linear networks (e.g., data collected over road networks or in river networks).

This family of methods includes techniques for:

  • Spatial and spatio-temporal data analysis, applicable to both geostatistical and point pattern data, including:
    • Nonparametric and semiparametric regression;
    • Generalized linear regression;
    • Quantile regression;
    • Density estimation;
    • Intensity estimation for inhomogeneous Poisson processes.
  • Functional data analysis over multidimensional domains, including:
    • Functional Principal Component Analysis and other dimensional reduction techniques;
    • Functional depth measures;
    • Functional clustering.

The course will cover:

  • Classical theory of nonparametric and semiparametric regression with roughness penalties, including basis expansion approaches
  • Parametric and nonparametric inference approaches;
  • An introduction to functional data analysis over multidimensional supports, focusing on Functional Principal Component Analysis (FPCA);
  • Strategies for handling missing data, in both spatio-temporal and functional settings.

Applications & Hands-On Learning

Case studies will showcase applications in environmental and life sciences. Practical lab sessions will utilize R package fdaPDE, available on CRAN (https://cran.r-project.org/web/packages/fdaPDE/index.html) and GitHub (https://github.com/fdaPDE).

Prerequisites

Master’s level knowledge of multivariate statistics.

Additional Resources

For further insights into this course and related topics: