https://scholar.google.com.ph/citations?user=F4gKTMkAAAAJ&hl=en
Title: Physics-enhanced machine learning for earthquake-induced landslide hazard mapping
Abstract: This project will introduce participants to advanced methods in landslide hazard mapping by coupling classical geotechnical models (Newmark's method for sliding displacements) with physics-informed machine learning (PINN) approaches.
Participants will:
· Explore how seismic shaking, slope stability, and soil parameters interact to trigger landslides,
· Develop machine learning models that incorporate physical constraints (e.g., Newmark's formulas) directly into the learning process,
· Compare traditional data-driven models with PINN-augmented models for landslide susceptibility mapping.
The group will blend theory, numerical simulation, and practical machine learning coding to better predict and understand earthquake-induced landslides.
Prerequisites:
· Basic knowledge of differential equations, soil mechanics, and slope stability,
· Familiarity with machine learning (Linear regression, SVM, RF, XGBoost, etc),
· Experience in Python programming (preferably with PyTorch or scikit-learn),
· Interest in geophysics, hazard modeling, and numerical simulation is a must.
https://www.researchgate.net/profile/Baba-Camara
Title: Deep learning of the connection graph driving the successful spread of invasive species
Abstract: This two-week research project investigates how deep learning can be used to infer and analyze the underlying connection graph that facilitates the successful spread of invasive species across spatial and ecological networks. Participants will explore how environmental, and biological factors contribute to species dispersal, and how these can be modeled as a graph where nodes represent habitats or regions and edges capture potential pathways of spread. Using real or simulated data, the team will implement graph-based deep learning models, such as Graph Neural Networks, to learn the structure and weights of these connections. The project aims to identify key transmission pathways, predict future spread patterns, and assess the influence of graph topology on invasion dynamics. Applications may span invasive plants, aquatic species, or agricultural pests.
Prerequisites:
· Basic understanding of machine learning and neural networks,
· Exposure to graph theory and network analysis concepts,
· Introductory knowledge of ecology or environmental modeling (helpful but not required),
· Familiarity with deep learning frameworks and programming proficiency.
https://www.uevora.pt/pessoas?id=5348
Title: Nonlinear hyperbolic systems of conservation laws: direct and regularized approximation methods
Abstract: This two-week research project focuses on the mathematical analysis of nonlinear hyperbolic systems of conservation laws, which arise in various fields such as fluid dynamics, traffic flow, and gas dynamics. Participants will study the existence, uniqueness, and behavior of weak solutions, including the formation of shocks and discontinuities. The project will explore both direct methods (e.g., Riemann solvers) and regularized approaches (e.g., vanishing viscosity) for approximating solutions. Through theoretical study, and eventually hands-on computational experiments, the group will compare the accuracy, stability, and efficiency of these methods, gaining insight into their applicability across different problem settings.
Prerequisites:
· Basic knowledge of ordinary and partial differential equations (especially in hyperbolic equations will be appreciated),
· Good mathematical analysis knowledge (e.g., implicit function theorem, and divergence theorem),
· Some familiarity with conservation laws with conservation laws will be appreciated,
· Some exposure to regularization techniques.
https://ymammeri.perso.math.cnrs.fr/
Title: Mathematical modeling of disease prevention with psychosocial factors by integrating game theory
Abstract: In this project, a group of 5-6 students will collaboratively develop mathematical models that incorporate psychosocial factors and strategic behavior in disease prevention. Using differential equations coupled with game theory, the team will explore how individuals’ decisions, driven by risk perception, motivation, and social influences, affect prevention measures like screening and lifestyle choices. The project will also introduce Physics-Informed Neural Networks as a modern tool to calibrate and refine the models using real-world data. This hands-on experience aims to equip students with interdisciplinary skills at the crossroads of mathematical modeling, behavioral science, and machine learning, preparing them for cutting-edge research in health sciences.
Prerequisites:
· Basic knowledge of ordinary differential equations,
· Familiarity with concepts of game theory (or willingness to learn),
· Interest in interdisciplinary applications involving mathematics, biology, and psychology,
· No prior experience in biology or neural networks required.
https://math.univ-lyon1.fr/~mercadier/
Title: Understanding environmental risks through extreme value theory
Abstract: This project brings together a group of students to explore mathematical and statistical methods for assessing risks for environmental extreme events (floods, storms, heatwaves) or for explaining human life span (taking into account environmental covariates). Participants will learn how extreme value theory can be applied to extrapolate phenomena until their extremal behavior. The project will combine theoretical concepts with data analysis and modeling techniques, providing practical experience in understanding and predicting environmental extremes or taking environmental information into account. This collaborative research effort aims to introduce students to cutting-edge tools at the intersection of modeling, statistics and environmental science.
Prerequisites:
· Knowledge of probability and statistics is preferred (population, sample, estimator, expectation, law of large numbers, central limit theorem),
· No prior experience in extreme value analysis is required,
· Interest in environmental sciences with no prior experience required,
· Basic programming skills (R or Python),
· Optional contribution upstream of the project: Could you provide any interesting demographic data from YOUR country covering several locations (age of the person at death, place of residence) and for which we could also have some environmental data (pollution, temperature, density, city or countryside)? If not, I will provide some, but I find it more interesting to look at the problem in South East Asia.
https://www.uevora.pt/pessoas?id=26227
Title: Flow and yield surface characterization of generalized Bingham fluids in complex geometries
Abstract: This project investigates the flow behavior and yield surface evolution of generalized Bingham fluids within complex geometries, including circular pipes with contractions and channels featuring sudden expansions. By integrating analytical approximations with numerical simulations, the study aims to characterize how key rheological parameters such as yield stress, consistency index, and flow index, affect the formation and extent of plug regions, velocity profiles, and overall flow patterns. Emphasis is placed on identifying critical transitions in flow regimes and understanding the interplay between geometry and non-Newtonian fluid properties.
Prerequisites:
· Fundamental knowledge of fluid mechanics,
· Familiarity with rheological models (e.g., Bingham, Herschel–Bulkley),
· Competence in calculus and differential equations,
· Experience with numerical methods (e.g., finite difference or finite element methods),
· Basic programming skills.
https://scholar.google.com/citations?user=DxZvvGUAAAAJ&hl=en
Title: A comparative study of regularization techniques in machine learning for community-based health screening tools
Abstract: This project explores the role of regularization techniques in enhancing the performance and generalizability of machine learning models for health screening in low-resource, community-based settings. Using osteoporosis as a case study, the project investigates how different regularization strategies, such as L1 (Lasso), L2 (Ridge), Elastic Net, and tree-based pruning, impact model behavior when applied to small-scale, imbalanced clinical datasets. Emphasis is placed on the mathematical foundations of regularization, including bias–variance trade-offs and penalty-based optimization. By comparing models such as logistic regression, decision trees, and ensemble methods (e.g., XGBoost), the study aims to identify the optimal regularization configurations that balance predictive performance, model interpretability, and feasibility for field-level deployment. The project further highlights the importance of simplicity and robustness in designing screening tools that can be adopted by non-specialist health workers.
Prerequisites:
· Basic understanding of supervised machine learning models (e.g., logistic regression, decision trees),
· Familiarity with regularization methods (e.g., Lasso, Ridge, pruning),
· Competence in linear algebra and optimization principles,
· Interest in health data analysis and practical algorithm design.
https://www.math.uzh.ch/compmath/en/stas?key1=105
Title: Numerical modelling of acoustic waves - practice and theory
Abstract: Abstract: This project focusses on important aspects for the modelling of acoustic waves and consists of four thematic blocks. Each of these blocks are split into three parts which are structured as follows:
a) A brief presentation of the essential principles of the numerical method.
b) An implementation session, where the participants implement the methods in Python.
c) Finally each block contains a final session with numerical experiments to study the sensitivity of the method.
While the theory is presented in general spatial dimensions, the implementation and numerical experiments are for problems which are reduced to 1D but still preserve the characteristic features.
Block 1: (5 1/2 days)
a) Short introduction: Modelling of acoustic waves:
a1) From physical principles to mathematical model problems (1/2 day).
a2) Finite Elements of polynomial order p in one dimension (1 day)
b) Implementation and numerical quadrature (3 days)
c) Sensitivity analysis of the discretization by numerical experiments. (1 day)
Block 2 (2 1/2 days).
a) Graded mesh: a tool to resolve solution with singularities. (1/2 day)
b) Implementation of graded meshes (1 day)
c) Numerical experiments (1 day)
Block 3. Adaptive methods (3 days)
a) A posteriori error estimate and adaptive finite elements. (1 day)
b) Implementation of the error estimator (1 day)
c) Numerical experiments for problems with singularities (1 day)
Block 4: Whispering Gallery Modes (2 days)
a) From regular oscillations to whispering gallery modes (1 day)
b) Implementation of whispering examples (1/2 day)
c) Systematic studies of convergence and computational complexity (1/2 day)
This schedule is preliminary and depends on the time needed to conduct the different blocks and will be adapted to the level of the participants.