Project Description
Project 1: We are interested in energy-driven pattern formation in multi-constituent physical and biological systems. The total energy of these systems includes two terms. The first term, called the growth part, favors large domains with minimum interface. The second term, called the inhibition part, prefers small domains. Exquisitely structured patterns arise as the balance of these two terms. Examples include morphological phases in block copolymers, animal coats, and skin pigmentation. Project 2: Neural networks are computational models inspired by the structure of the human brain, capable of learning from data and making predictions or decisions. Physics-informed neural networks (PINNs) are a machine learning approach that incorporates physical laws into the learning process of neural networks. Unlike traditional neural networks that primarily rely on data-driven methods, PINNs combine data with physical constraints (such as partial differential equations and ordinary differential equations) to enhance their modeling capability and prediction accuracy for complex scientific problems.
Prerequisites
Having knowledge in multivariable calculus and ODEs will be an advantage. Or you are willing to spend extra time to learning them.
Special Comments
Project Information (subject to change)
Estimated Start Date: 6/2/2025
Estimated End Date: 8/8/2025
Estimated Project Duration: 10 weeks
Maximum Number of Students Sought: 3
Research Location: Hybrid
Contact Information: Chong Wang (email: cwang@wlu.edu)