University of Oxford
Mathematical Institute

Developing smarter ways to find the best solution to complex problems

Optimisation lies at the core of many technological challenges, including training neural networks, planning robot motion and calibrating financial models. These tasks often involve finding the best solution among an enormous number of possibilities. However, the landscape of possible solutions can be highly complex, making it difficult to find the best overall result. Traditional gradient-based algorithms can struggle to navigate these landscapes, particularly when gradients are unavailable, noisy or expensive to calculate.

Yuyang’s research will develop a gradient-free framework for global optimisation. She will combine ideas from optimal control, which steers a search towards globally optimal solutions, with interacting particle systems that explore the landscape collectively, much like a swarm sharing information. She will also develop dimensionality-reduction techniques that represent high-dimensional problems using simpler, lower-dimensional structures, improving the efficiency and scalability of both approaches.

Together, these methods aim to strengthen the mathematical foundations and practical performance of global optimisation algorithms. Potential applications range from protein folding and aerodynamic design to structural engineering, where more effective optimisation could improve performance and make better use of computational and material resources.