Schedule: Please see here
Course content:
The school consists of six courses. Without overlapping, the proposed courses are complementary and cover a wide range of topics in industrial mathematics as well as modeling, theoretical, numerical, computational and simulation aspects. Participants will be shown why mathematics is crucial for solving real-world problems in the context of explicit industry and/or societal challenges. Each participant will attend all courses and undertake a mini-project related to one of the course topics (this will last throughout the course). Moreover, several talks (and a round table) regarding applied and industrial mathematics in a broader sense are planned to expand the attendees experience and provide the opportunity for a large discussion forum.
1. Mark Asch, “Physics Augmented Machine Learning for Industrial Applications”
This course prepares for the use of machine learning in industrial applications, where the underlying mechanistic models are exploited conjointly. We will begin by surveying the most commonly used methods of supervised, unsupervised and reinforcement machine learning techniques. We will briefly cover some useful deep learning techniques, such as encoders and convolutional neural networks. Then we will explore the conjoint use of physics to enhance the machine learning models, and guarantee that the solutions obtained are indeed physically pertinent. The approaches for this enhancement will include feature and layer engineering, physics induced neural networks (PINN), and surrogate modeling. The lectures will be illustrated by industrial applications and will be complemented by practical coding tutorials.
2. Joaquim M. C. Correia, “Modelling with hyperbolic systems of conservation laws”
In this course real-world problems provide motivation for the mathematical concepts/theory of hyperbolic systems of conservation laws. In particular we will consider a few examples presented at some ESGI (European Study Groups with Industry) meetings. Here is a list of topics under consideration: 1) Euler’s compressible gas dynamics (first order conservation laws): shock waves, Rankine-Hugoniot condition, hyperbolicity, and entropy criteria; 2) pollutant effects on stone monuments (convective, diffusive and capillary mechanisms): porous-capillary media; 3) image processing (denoising and segmentation): nonlinear diffusions; 4) reacting gas flows or coagulation-fragmentation theory: approximations and the viscosity-capillary vanishing method.
3. Youcef Mammeri, “Modeling waterborne diseases: mathematical formulation and numerical implementation”
This lecture presents an integrated approach to model the transmission of waterborne diseases by linking epidemiological dynamics, hydrological processes, and water management strategies. Outline: 1) introduction to waterborne diseases; 2) environmental and epidemiological modeling (SIR and Ross-MacDonald-style models with environmental compartments); 3) hydrological modeling (advection-reaction-diffusion, flooding, canals, and irrigation systems); 4) water quality dynamics and pathogen survival (chemostat models, chlorination, sedimentation); 5) optimal water management (incorporating chlorination and sanitation interventions as control variables); 6) PINNs (coupled epidemiological-hydrological systems with sparse data, application to cholera risk during Mekong delta floods).
4. Tim Myers, “Practical applications of Moving Boundary Problems”
Moving boundary problems (MBPs) are a class of mathematical problems where the domain changes with time and is initially unknown - consequently it must be determined as part of the solution process. This dynamic nature makes them complex, but they are crucial for modelling a vast array of real-world phenomena such as phase change (melting, evaporation etc), crystal growth, clogging of arteries, tissue growth, pollutant transport, crack propagation and even mathematical finance. In this course we will start from the basic formulation, learning about modelling and techniques and then apply the knowledge to problems of current industrial interest.
5. Marília Pires, “Numerical Simulation in Python of Newtonian and Non-Newtonian Laminar Flow in Pipes with Applications to the Food and Cosmetics Industry”
In the food industry, the transport of viscous liquids, such as syrups, thick syrups, oils, sauces, pulps, or creams, through pipelines is a central process. The ability to control the velocity profile and pressure losses of Newtonian fluids, as well as non-Newtonian fluids described by the Power-Law model, is crucial for the proper sizing of pumps and for minimizing energy consumption. This case study seeks to apply Python to numerically solve the laminar flow of a Newtonian fluid in a cylindrical pipe, to determine the resulting velocity profile, and to estimate the associated pressure drops by means of numerical methods (FDM) or even direct ODE solvers.
6. Thi Minh Thao Le, “Modeling and Data-Driven Inference in Infectious Disease”
This lecture presents an integrated framework for modeling infection dynamics by linking coinfection SIS models, replicator equations, and data-driven inference methods. The lecture will cover: 1) quasi-neutral dynamics in coinfection systems and their equivalence to replicator equations; 2) applications to Streptococcus pneumoniae, including inference of pairwise strain interactions from frequency data across settings and analysis of context-dependent mutual invasibility; 3) vaccination works, including bottleneck-size estimation and selection tests based on biological diversity data; 4) selection models and data-driven inference for S. pneumoniae using from exponential model, logistic model to Lotka-Volterra and replicator dynamics; 5) applications to Escherichia coli, focusing on how species frequencies in a host environment can modulate selection coefficients between strains, and how machine-learning algorithms and multiobjective optimization can be used to predict relative fitness in new environments, steer selection, and design strategies to reduce antimicrobial resistance in microbiomes.