Project Description

Physics-Informed Neural Networks (PINNs) are a novel class of deep learning models that incorporate physical laws and principles into their structure, enabling them to learn from data while respecting the underlying physics of the problem. By integrating differential equations that represent physical laws into the loss function, PINNs can effectively learn from sparse and noisy data, making them a powerful tool for scientific computing and engineering problems. Multiscale problems are prevalent in various fields such as process systems engineering, electrical engineering, and fluid mechanics. These problems involve phenomena that occur at different scales, both in time and space, and require sophisticated models to accurately capture the interactions between these scales. For instance, in process systems engineering, the design and optimization of chemical processes often involve phenomena at the molecular, unit operation, and plant-wide scales. Similarly, in fluid mechanics, understanding the behavior of fluids requires models that can capture interactions from the molecular scale to the macroscopic flow patterns. PINNs, with their ability to incorporate physical principles, present a promising approach to tackling these multiscale problems. They can be designed to respect the laws of physics at each scale, providing a unified framework that can capture the multiscale nature of these problems. This makes PINNs a potentially transformative tool for multiscale modeling in various engineering and scientific disciplines. This project aims to develop novel PINNs for addressing complex multiscale engineering systems.

Start Date

After February, 2024

Postdoc Qualifications

PhD in applied math, computer science, industrial engineering, chemical engineering, electrical engineering, mechanical engineering, or related fields.
Fluent programming in one of the following programming languages: Python/Julia/C++.

Co-Advisors

Name: Can Li
email: canli@purdue.edu
Affiliation: Davidson School of Chemical Engineering
website: https://canli1.github.io/


Name: Guang Lin
email:guanglin@purdue.edu
Affiliation: Departments of Mathematics, Statistics & School of Mechanical Engineering
Website: https://www.math.purdue.edu/~lin491/ 

Short Bibliography

Leung, W. T., Lin, G., & Zhang, Z. (2022). NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems. Journal of Computational Physics, 470, 111539.
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021). Physics-informed machine learning. Nature Reviews Physics, 3(6), 422-440.
W. Deng, X. Zhang, F. Liang, G. Lin. An Adaptive Empirical Bayesian Method for Sparse Deep Learning. NeurIPS 2019
Hubbs, C. D., Li, C., Sahinidis, N. V., Grossmann, I. E., & Wassick, J. M. (2020). A deep reinforcement learning approach for chemical production scheduling. Computers & Chemical Engineering, 141, 106982.