###Neural networks for stochastic partial differential equations
Project ID: 2228bd1127 (You will need this ID for your application)
Research Theme: Mathematical Sciences
UCL Lead department: Mathematics
Lead Supervisor: Hao Ni
Project Summary:
Stochastic partial differential equations (SPDEs) are useful building blocks to model random spatiotemporal dynamics, which have broader applications ranging from weather forecasting to fluid dynamics. The recent advance in applying machine learning (ML) to learn SPDE solutions has drawn increasing attention, due to its superior capacity to accelerating the SPDE solver. Moreover, the generalization of physics- informed neural networks from PDEs to SPDEs may provide a novel family of neural networks for analysing noisy spatiotemporal data, which can be used to discover the hidden physics law and predict the future data evolution.
What you will be doing:
Regularity structure, as Fields medallist’s work, provides a mathematically rigorous framework to define the solution to a large family of SPDEs. In this project, you will design novel and principled neural networks by incorporating regularity structure, to improve the accuracy and efficiency of the SPDE solver. You will establish the theoretical foundations for the proposed networks and/or validate the effectiveness of the proposed model on a number of SPDE examples by benchmarking with the conventional SPDE solvers and state-of-the-art ML models. Moreover, you will generalize the physics-informed neural networks to the SPDE cases for model calibration and prediction of spatiotemporal data.
Who we are looking for:
The candidates are supposed to have (1) solid backgrounds in mathematics and machine learning and (2) strong programming skill. The candidates should have problem-solving and fast learning skills.