The Power of Data in Partial Differential Equations Models
Partial differential equations (PDEs) describe a wide variety of phenomena such as sound, heat, elasticity and quantum mechanics. Data science and theories on differential equations have been evolving, but interactions between data science and differential equations have been rare.
This project examines physical systems by fusing machine learning approaches with PDE systems. For example, PDE models that are not derived from the first principles, often include empirical parameters. The key to most inverse problems is to accumulate appropriate data that contains the needed information to recover the empirical parameters. Data science techniques can be used to efficiently determine the empirical parameters using measurements.
Qin Li, Assistant Professor of Mathematics