Neural network methods stellarators equilibrium Optimization in nuclear fusion

Neural network based methods for stellarators equilibrium Optimization in nuclear fusion

The internship focuses on the numerical construction of magnetic equilibria in stellarators
, devices where the three-dimensional geometry of the coils directly imposes the helical structure of the magnetic field. Computing an equilibrium means determining the closed magnetic surfaces and the associated physical quantities—such as the rotational transform, pressure profile, and geometric characteristics of the flux surfaces—that satisfy the stationary MHD equilibrium equations. These equilibria are essential for understanding confinement properties, stability, and the geometric optimization of stellarators.

The goal of the project is to build a parametrized model capable of generating entire families of 3D stellarator equilibria as shape or physics parameters vary. To represent the highly twisted, quasi-periodic geometry of stellarator flux surfaces, we aim to learn an adapted coordinate transformation
, combining a Fourier representation (naturally suited to toroidal–poloidal periodicity) with an invertible neural network (able to model fine, smooth, and bijective deformations). This hybrid Fourier + invertible-network parameterization matches the intrinsic structure of stellarators, balancing analytic structure with the flexibility of learned transformations.

Training will rely on natural gradient optimization
, which is more appropriate than standard gradient descent when optimizing geometric objects or nonlinear coordinate mappings. Ultimately, the project aims to produce a tool capable of rapidly generating parameterized families of stellarator equilibria, thereby enabling fast exploration, optimization, and analysis of complex configurations beyond what traditional equilibrium solvers can easily provide.

• Formulate the optimization problem forstellarators equilibrium
• propose diferent architectures of neural network approximation space (invertible or not)
• formulate the training with Natural Gradient solver
• Implement in the torch Library Scimba the problem
• Validate on reference test cases
• Go to parametric problems in large dimension

• Scientific computing for PDEs
• strong ability in Python programming
• (Optional) Basic electromagnetics or fluid mechanics

• 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