Stochastic Flow Paths for Fast Hazard Simulation

Le descriptif de l’offre ci-dessous est en Anglais_

**Niveau de diplôme exigé**: Bac + 5 ou équivalent

**Fonction**: Stagiaire de la recherche

**A propos du centre ou de la direction fonctionnelle**:
Inria is the French National Institute for Research in Digital Science, of which the Inria Côte d'Azur University Center is a part. With strong expertise in computer science and applied mathematics, the research projects of the Inria Côte d'Azur University Center cover all aspects of digital science and technology and generate innovation. Based mainly in Sophia Antipolis, but also in Nice and Montpellier, it brings together 47 research teams and nine support services. It is active in the fields of artificial intelligence, data science, IT system security, robotics, network engineering, natural risk prevention, ecological transition, digital biology, computational neuroscience, health data, and more. The Inria Center at Université Côte d'Azur is a major player in terms of scientific excellence, thanks to the results it has achieved and its collaborations at both European and international level.

**Mission confiée**:
**Context and goal**

Natural hazards such as flash floods, debris flows, or landslides are difficult to anticipate in real time. Existing numerical simulation methods rely on small time steps to guarantee stability, which makes them too slow to cover the large spatial and temporal scales required during emergencies [1]. As a result, decision makers often lack accurate predictive tools when rapid response is most critical.
A promising research direction is to exploit the geometric structure of gravity-driven flows. Instead of simulating the evolution of the entire flow field at small time steps, we can track stochastic flow paths — curves that follow the dominant directions of the fluid over long distance. This idea is inspired by meshless Monte Carlo solvers in computer graphics [2]. By reformulating the shallow water transport equations along these paths, we can design solvers that use very large time steps while preserving essential physical behavior.
The objective of this internship is to develop and evaluate a Monte Carlo flow path solver for fast, uncertainty-aware simulation of shallow flows over complex terrains.

**Approach**
The internship will focus on the mathematical and algorithmic foundations of stochastic flow path simulation, through the following steps:

- Flow path formulation: Recast shallow-water transport as implicit equations along flow paths. Represent uncertain flow directions with local probability distributions, and compute upstream

fluxes by sampling these distributions (See the random receiver selection in [3] for a simple example). - Monte Carlo solver design: Implement a stochastic fixed-point algorithm that iteratively updates flow thickness and velocity distributions. We will look in particular at how to add a memory effect between the iterations to stabilize the convergence.
- GPU acceleration: Adapt techniques from flow routing and path tracing to efficiently sample and accumulate contributions along flow paths. Explore parallelization strategies to enable large-scale simulations [4].
- Validation and analysis: Compare

**Principales activités**:
Main research activities:

- Bibliography study
- Implementation of a prototype and experiment
- Analysis of the results
- Scientific communication

**Compétences**:
Computer Graphics, Machine Learning

PDE and physical simulation is a plus

C/C++, Cuda, Python

**Avantages**:

- Subsidized meals
- Partial reimbursement of public transport costs
- Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
- Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
- Professional equipment available (videoconferencing, loan of computer equipment, etc.)
- Social, cultural and sports events and activities
- Access to vocational training

**Rémunération**:
Traineeship grant depending on attendance hours.

**Informations générales**:

- **Thème/Domaine**: Interaction et visualisation
Calcul Scientifique (BAP E)
- **Ville**: Sophia Antipolis
- **Centre Inria**: Centre Inria d'Université Côte d'Azur
- **Date de prise de fonction souhaitée**: 2026-02-02
- **Durée de contrat**: 7 mois
- **Date limite pour postuler**: 2025-11-02

**Consignes pour postuler**:
**Sécurité défense**:
Ce poste est susceptible d’être affecté dans une zone à régime restrictif (ZRR), telle que définie dans le décret n°2011-1425 relatif à la protection du potentiel scientifique et technique de la nation (PPST). L’autorisation d’accès à une zone est délivrée par le chef d’établissement, après avis ministériel favorable, tel que défini dans l’arrêté du 03 juillet 2012, relatif à la PPST. Un avis ministériel défavorable pour un poste affecté dans une ZRR aurait pour conséquence l’annulation du recrutement