Physics-Informed Neural Networks

The towering emergence of AI is currently permeating every corner of science and engineering. By digesting large amounts of data, AI methods can distill complex relationships between observable and hidden variables, and allow us to build predictive tools that are currently transforming entire scientific fields, from computer vision and robotics, to natural language processing and structural biology. However, there still exists a vast number of scenarios for which observational data may be incomplete and/or expensive to acquire, rendering the reliable use of current AI models extremely challenging.  

But there is hope. One key insight here is that the natural world around us evolves according to the stable laws of physics. So how do we bring in physics and domain knowledge to design AI systems that can learn smarter, faster and more accurately from fewer training examples? Physics-informed neural networks (PINNs) provide a way for doing so by ensuring that the predictions of a neural network are compatible with the physical laws that govern our observations. This additional structure can compensate for the lack of training data, and even allows us to rapidly predict quantities that we may not be able to directly measure (e.g. predict the blood pressure in our arteries from indirect MRI measurements of blood velocity). 

This technology is currently a key enabler across a collection of cutting-edge applications, from non-destructive materials testing and designing microelectronic devices, to improving X-ray scans and understanding tissue mechanics in a beating heart. But as with any emergent technology, the possibilities are endless and an ocean of applications still remains to be explored. 

The Predictive Intelligence Lab is the research team of Professor Paris Perdikaris at the department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania. Our members have interdisciplinary backgrounds and they work at the intersection of engineering, scientific computing and AI. Our work spans a wide range of areas in computational science and engineering, with a particular focus on the analysis and design of complex physical and biological systems using machine learning, computational mechanics and high-performance computing. Current research interests include physics-informed machine learning, uncertainty quantification, and engineering design optimization. For more details, please see our recent work here. 

POPULAR SCIENCE ARTICLES

Quanta; Latest Neural Nets Solve World’s Hardest Equations Faster Than Ever Before

ASCR Discovery; Lessons Machine-Learned

Penn Engineering; Paris Perdikaris Predicts Complex Outcomes of Physical Systems

Penn Today; Refining Data Into Knowledge, Turning Knowledge Into Action

ORIGINAL RESEARCH PAPERS:

Nature Reviews Physics, Physics-informed machine learning

Journal of Computational Physics, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.