PhD Position: Numerical Methods for Highly Oscillatory Time Dynamics

This PhD position at Inria Rennes focuses on advancing numerical methods for solving highly oscillatory time dynamics, a critical challenge in computational science. The project, funded by ANR and in collaboration with Inria Macaron (Strasbourg), aims to integrate machine learning—specifically autoencoders—to capture rapid dynamics in complex systems. The successful candidate will conduct state-of-the-art reviews, analyze existing numerical schemes, and propose novel hybrid approaches combining traditional and AI-driven techniques. The work will involve programming, publishing research, and presenting findings at international conferences. This opportunity is ideal for researchers passionate about bridging numerical analysis and machine learning.

• Conduct a comprehensive literature review of existing numerical methods for solving highly oscillatory differential equations.
• Analyze and compare standard numerical schemes to identify limitations and bottlenecks in current approaches.
• Develop and implement novel numerical methods combining traditional techniques with machine learning (e.g., autoencoders) to capture rapid dynamics.
• Program and test the proposed methods using high-performance computing tools and frameworks.
• Write and publish research papers detailing findings and methodologies in peer-reviewed journals and conference proceedings.
• Present research results at international conferences and workshops related to numerical analysis and scientific computing.
• Collaborate with the Inria Macaron team in Strasbourg to integrate findings into broader project objectives.