Course content

Part A: Traditional Multivariate and Time-Series Methods

• Multiple Linear Regression
• Principal Component Analysis (PCA)
• Principal Component Regression (PCR)
• Partial Least Squares Regression (PLSR)
• Support Vector Machine (SVM)
• Independent Component Analysis (ICA)
• Time-series analysis methods
• Clustering and unsupervised learning methods
• Outlier detection methodologies and robust statistics

Part B: Deep Learning Methods

• Fundamentals of neural network architectures
• Autoencoders for representation learning and dimensionality reduction
• Transformer architectures for sequence modelling and attention mechanisms
• Diffusion models for generative modelling and probabilistic inference

Part C: Hybrid and Physics-Informed Modelling

• Physics-Informed Neural Networks (PINNs)
• DeepONets and operator learning
• Compressed sensing and sparse recovery
• Corrective Source Term approaches in data-driven physical modelling
• Dynamic Mode Decomposition (DMD) for dynamical systems analysis

Learning outcome

Cognitive Learning Outcomes (Knowledge and Skills)

By the end of this course, students will be able to:

• Explain the principles, assumptions, and mathematical foundations of traditional multivariate analysis, deep learning methods, and hybrid modelling techniques.
• Apply PCA, ICA, PLSR, FFT/EMD, clustering algorithms, and outlier detection to real-world datasets for exploratory and predictive analysis.
• Construct and train neural network models, including autoencoders, transformer-based architectures, and diffusion models.
• Analyse and interpret the behaviour and performance of deep learning models in relation to dataset structure, overfitting, generalisation, and optimisation challenges.
• Integrate physics-based constraints and machine-learning techniques by implementing PINNs, DeepONets, compressed sensing frameworks, and DMD-based models.
• Evaluate model performance using appropriate statistical and numerical metrics, considering robustness, interpretability, and computational cost.
• Select and justify appropriate modelling approaches for a given problem, based on data characteristics, domain knowledge, and methodological constraints
• Use AI tools responsibly to support self-directed learning, including generating code examples, exploring new analytical methods, and critically evaluating AI-generated suggestions.

Non-Cognitive Learning Outcomes (Professional Competencies)

Students completing this course will:

• Develop critical thinking regarding modelling choices, algorithmic limitations, and the interpretability of data-driven results.
• Demonstrate independence and confidence in conducting end-to-end data analysis, from preprocessing to model selection and validation.
• Exhibit responsible and reflective practice, recognising when models may fail, identifying sources of uncertainty, and understanding the implications of data misuse.
• Collaborate effectively in multidisciplinary contexts, bridging domain expertise with analytical and computational perspectives.
• Strengthen creativity and adaptability in combining classical and modern modelling approaches to design hybrid solutions for complex systems.
• Cultivate ethical awareness and digital responsibility in the use of AI tools for learning, ensuring transparency, verification, and critical judgment when relying on AI-generated content.

Learning methods and activities

The course employs a combination of interactive, practice-oriented, and exploratory learning methods designed to support both conceptual understanding and hands-on competence in data analysis. Teaching is centered around the use of interactive Python notebooks, enabling students to work directly with algorithms, visualizations, and datasets while receiving immediate feedback through experimentation and iterative refinement.

Students complete take-home assignments that promote deeper reflection, independent problem-solving, and the application of analytical methods to realistic scenarios. These assignments reinforce theoretical concepts by requiring their implementation, evaluation, and interpretation in code.

A key component of the course is the use of AI-assisted coding tools. Students will be shown how artificial intelligence can support the creation, debugging, and optimization of data analysis workflows. This includes demonstrations of how AI can help generate code, suggest alternative modelling strategies, and accelerate exploratory analysis—while also discussing limitations, best practices, and issues related to reliability and transparency.

The course additionally includes live demonstrations with real-world data, where full modelling workflows are performed and discussed. These demonstrations expose students to practical challenges such as data cleaning, feature extraction, model tuning, and the interpretation of analytical results. They also provide opportunities for discussion, questions, and collaborative exploration of different methodological choices.

Together, these learning activities foster active engagement, strengthen technical proficiency, and promote critical thinking about model behaviour, data quality, methodological trade-offs, and the responsible use of AI tools in data analysis.

Compulsory assignments

• compulsory exercise

Recommended previous knowledge

Basic knowledge about linear algebra.

Required previous knowledge

Good understanding of basic linear algebra.

Course materials

The course material will be presented at the start of the course