Guiding Hyperparameter Choices in Hybrid PDE Solvers with Large Language Models

Guiding Hyperparameter Choices in Hybrid PDE Solvers with Large Language Models Level of qualifications required : Graduate degree or equivalent Fonction : Internship Research Context Modern numerical simulation codes, especially those combining classical scientific computing and machine learning components, rely on a large number of hyperparameters that strongly impact accuracy, stability, and computational efficiency. These parameters are often tuned manually using empirical rules and expert intuition, an approach that becomes increasingly inadequate as code complexity grows. This internship aims at exploring the use of large language models (LLMs) as optimization agents to assist and partially automate hyperparameter selection in hybrid simulation codes. The LLM interacts with a numerical solver for a convection–diffusion equation discretized using finite differences and coupled with a neural network–based preconditioner. At each iteration, the LLM proposes a new set of parameters, simulations are executed, and performance metrics (convergence, stability, computational cost, accuracy) are summarized into a reward signal. Guided by this feedback, the LLM iteratively refines its proposals. The work will first focus on hyperparameters of the numerical solver and learning components, and may later be extended toward constrained AutoML for the neural network architecture. Throughout the process, certification criteria are enforced to ensure that the numerical behavior of the solver is not degraded. The convection–diffusion problem serves as a simple testbed to establish a robust methodology before targeting more complex simulation codes. Main activities SOTA on optimization with LLM Construct of simple 1D finite difference code with neural network based preconditionning Conception of metric for solver evaluation Optimization of the hyparameters by LLM andFeedback-Guided Prompting AutoML extension using the LLM Validation Skills Basics of PDEs and numerical methods (finite differences, stability) Fundamentals of machine learning and hyperparameter tuning Experience with Python and scientific libraries (NumPy, SciPy, PyTorch/JAX) Ability to analyze simulation metrics Interest in LLMs and prompting Benefits package 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 Theme/Domain :Optimization, machine learning and statistical methodsScientific computing(BAP E) Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inria website. Processing of applications sent from other channels is not guaranteed. Instruction to apply Defence Security :This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment. Recruitment Policy :As part of its diversity policy, all Inria positions are accessible to people with disabilities. Inria is the French national research institute dedicated to digital science and technology. It employs 2,600 people. Its 200 agile project teams, generally run jointly with academic partners, include more than 3,500 scientists and engineers working to meet the challenges of digital technology, often at the interface with other disciplines. The Institute also employs numerous talents in over forty different professions. 900 research support staff contribute to the preparation and development of scientific and entrepreneurial projects that have a worldwide impact. #J-18808-Ljbffr