Anurag Kamal is a master’s student in mechanical engineering at the Michigan Technological University. After working for an automotive OEM toward the development of automated powertrains, his current interest lies in our electric powertrains of electric vehicles. His primary area of research is toward the modeling of batteries for electric vehicles. Overwhelmed with the entrepreneurial exposure at Michigan Tech, Anurag plans to commercialize his research for building an energy storage company.
Project: Teaching Neural Nets to Solve Partial Differential Equations
The goal of this work is to train neural networks to solve partial differential equations (PDEs) more efficiently than the existing numerical methods. The proposed method can do faster estimations and solve for conditions where other estimations do not converge.
Main Results in Detail
The initial equation modeled for validation was a modified form of Fick’s law of diffusion for a variety of regions made using a convex mesh hull. The model was trained using a seven-layer network for colored images and then increased to 25 layers for different sizes of black and white images. The model was extended to splines and then time-dependent nonlinear equations in multiple dimensions for varying of the coefficient c, and then predictions were made for our range of values.
- 1. Studying the efficacy of this learning for other nonlinear partial differential equations.
- 2. Exploring different network architectures.