Ph.D. student (M/F) in computer graphics and thermal simulation for infrared rendering

Job Description

Thesis Subject

The IRIT STORM team, specialized in computer graphics (https://www.irit.fr/storm/site/), is looking for a doctoral student as part of the MC-OP project funded by the CNRS through the MITI interdisciplinary programs, in collaboration with the LAPLACE GREPHE team, specialized in energetics (https://www.laplace.univ-tlse.fr/grephe/).

Context :
Realistic rendering in image synthesis and thermal simulation in physics rely on a similar formulation of the problem to be solved and an identical resolution method: a probabilistic formulation of the transport problem and Monte Carlo methods for its resolution. These numerical methods are the only ones capable of addressing multi-physics and multi-scale problems (e.g., urban heat islands). The operational effectiveness of these methods depends on the joint development of: the formulation of the considered physics in a path space, led by the physics community, and the construction of these paths in complex geometries, work carried out by the computer graphics community.
Thus, heat transfers have recently been expressed based on "thermal paths" [5] (by the physics community), which are an alternation between conductive paths (transport via Brownian motion), convective paths (transport via flow), and radiative paths (transport via radiation), coupled within a single path space. By leveraging efficient path construction methods in complex geometries (developed by the computer graphics community), these thermal paths have enabled the development of an infrared rendering method, which already addresses strong industrial and academic challenges. However, certain limitations prevent its full operational deployment. It is within this context of infrared image synthesis through thermal simulation in path space that this PhD thesis in computer graphics is positioned.

Scientific bottlenecks :
The main limitations of the method, which arise in certain situations, include:
- Impractical computation time due to the trapping of certain paths in sub-parts of the system (typically in metallic conductors or extremely thin elements);
- The presence of non-linearities in one or more models or in the coupling between models, which poses a major theoretical challenge when translating into a statistical path space (as well as a source of bias when these paths must be truncated due to branching that reflects non-linearity);
- Residual bias in some of the most essential estimators (e.g., Brownian motion in confined environments, even in the absence of non-linearities).
The primary focus of this thesis will be the latter limitation, specifically the reformulation of probabilistic models at the interfaces of solids, which are problematic due to the biases they introduce in calculations (whether from non-linearities or numerical parameters). In particular, coupling Brownian motion with other transfer modes across the interfaces of solid parts is a notoriously difficult problem. Current schemes based on spatial discretization introduce a numerical parameter. However, standard solutions for reducing biases through numerical parameters have not yielded satisfactory results. This leads us to completely rethink how these couplings occurring at interfaces should be handled.

Thesis Objectives :

Recent work in computer graphics has specifically addressed the challenge of completely removing bias from stationary diffusion schemes described in path space (Brownian motion), with the goal of making them operational in complex geometry. These approaches build their theoretical foundations on recent advancements in applied mathematics literature on Monte Carlo methods and introduce new computational abstractions designed for constructing novel paths in complex geometries. These methods form the primary theoretical framework upon which our own interface schemes will be developed, taking into account our objectives and constraints:
1. In the aforementioned works, physical domain interfaces are treated as simple boundary conditions. However, in the context of coupled thermal simulations, interfaces become the site of coupling, and paths will continue by switching from one transfer mode to another, introducing new constraints.
2. There is an immediate need to account for the transient nature of heat transfers, unlike the steady-state approaches typically used by the computer graphics and mathematics communities.
3. It is essential to preserve the physical meaning associated with paths in terms of causal propagation. Visualizing these paths allows for the interpretation of the underlying mechanisms — how energy is transported through space and time from sources to sensors — enabling, for example, the analysis of infrared images.
From a modeling perspective, the thesis will focus on formulating new interface schemes tailored to our coupled thermal simulation context. These schemes will ideally be unbiased, or their bias will be fully characterized.
From an algorithmic operational perspective, the efficient construction of paths may require the implementation of data structures optimized for recurrent geometric queries, as well as variance reduction strategies.

Skills :
The PhD candidate must hold a Master's degree or an engineering degree in computer graphics, applied mathematics, or fundamental or energy physics, as well as:
- Experience in modeling and in C/C++ programming;
- Knowledge in probability, statistics and Monte Carlo methods for rendering (path-tracing);
- Analytical and problem-solving skills;
- Strong written and oral communication skills in both English and French;
- Aptitude for interdisciplinary work and team collaboration.
Skills or experiences in the following areas will be considered as a plus :
- Physical modeling and simulation;
-Scientific computing and partial differential equation solving.

Your Work Environment

The thesis will be conducted within the STORM team at IRIT (https://www.irit.fr/).
The thesis will also be held in close collaboration with the GREPHE team at LAPLACE (https://www.laplace.univ-tlse.fr/). Both laboratories are located on the Paul Sabatier University campus, just a few minutes' walk apart. The affiliated doctoral school will be « École Doctorale Mathématiques, Informatique, Télécommunications de Toulouse » (https://ed-mitt.univ-toulouse.fr/as/ed/edmitt/page.pl).
For more details : M. Bati et al. « Coupling Conduction, Convection and Radiative Transfer in a Single Path-Space: Application to Infrared Rendering ». ACM Trans. Graph. 2023.

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

CNRS

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