Predictive Science Laboratory

About Us

We are a research laboratory at the School of Mechanical Engineering of Purdue University, founded in 2014 by Dr. Ilias Bilionis.

Mission

Our mission is to develop scientific machine learning technologies to accelerate engineering innovation.

Philosophy

We operate at the intersection of mathematics, statistics, and engineering, facilitating communication between these disciplines by employing Bayesian probability and an additional layer of causality expressed through differential equations.

Basic Research Areas

Uncertainty propagation through high-dimensional stochastic differential equations: e.g., (Tripathy et al., 2016), (Karumuri et al., 2020).
Bayesian inverse problems: e.g., (Bilionis et al., 2013), (Karumuri et al., 2023).
Sequential design of experiments: e.g., (Pandita et al., 2016), (Pandita et al., 2016).
Information field theory as a unified paradigm for uncertainty quantification. This is where most of our efforts are at the moment. To learn more read the papers: (Alberts et al., 2023) (Hao et al., 2024). Or watch this video from a recent talk at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK:

Current Projects

Bayesian hemodynamic flow reconstruction from imaging modalities using information field theory (NSF).
Subcutaneous and intrathecal drug delivery (Eli Lilly): e.g., (de Lucio et al., 2023), (Sree et al., 2023).
Electric machines (Ford): e.g., (Beltrán-Pulido et al., 2022), (Beltrán-Pulido et al., 2020).
Design of corrosion-resistant high-entropy alloys (NSF): e.g., (Karumuri et al., 2023)
Thermal insulation for hypersonic vehicles (AFRL): e.g., (Thomas et al., 2024), (Karumuri et al., 2024).
Uncertainty quantification in combustions modeling (Cummins): e.g., (Zinage et al., 2022).
Smart buildings (NSF): e.g., (Kim et al., 2022), (Kim et al., 2023).
Extra-terrestrial habitats (NASA): e.g., (Dyke et al., 2021), (Maghareh et al., 2021)

Funding

Our funding comes from NSF, NASA, DARPA, AFRL, Eli Lilly, Cummins, and Ford.

Teaching

Bilionis loves teaching scientific machine learning, probabilistic thinking, and uncertainty quantification to engineers. Some examples are these:

ME 697 - Advanced Scientific Machine Learning is offered on-campus during Spring 2024. You can find the online textbook here. But it is a work in progress.
ME 539 - Introduction to Scientific Machine Learning is being offered during Spring 2024 both online. You can find the online textbook here.
ME 297 - Introduction to Data Science for Mechanical Engineers. This was offered for the last time during Spring 2023. You can find the online textbook here.
ME 597 - Introduction to Uncertainty Quantification. Bilionis taught this for the last time in Spring 2020. About one third of the topics taught there made it into ME 539. However, this course contains some classical uncertainty quantification lectures that Bilionis could not fit in the new course. You an find the video lectures here.
A hands-on introduction to physics-informed machine learning. This is a short lecture on the topic. You can find the Jupyter notebook here.

People

Ilias Bilionis

Professor of Mechanical Engineering

Purdue University

ibilion@purdue.edu

Google Scholar

Short bio

Personal GitHub profile

Lab GitHub

Akshay Jacob Thomas

Postdoctoral Researcher

Bayesian inverse problems, Physics informed neural networks, Digital twins for advanced manufacturing

Google Scholar

Alexander Alberts

Postdoctoral Researcher

Physics-informed, information field theory

Kairui Hao

Postdoctoral Researcher

Physics-informed, information field theory for dynamical systems

Atharva Hans

Postdoctoral Researcher

Superresolution of 4D flow MRI using information field theory

hans1@purdue.edu

Google Scholar

Personal GitHub profile

Andrés Felipe Beltrán-Pulido

Ph.D. Student

Purdue University

beltranp@purdue.edu

Electric machine design optimization using physics informed neural networks

Google Scholar

Personal GitHub profile

Rudra Sethu Viji

Ph.D. Student

Information field theory for fluid flow reconstruction from non-intrusive flow measurements

Sreehari Manikkan

Ph.D. Student

Digital twins for smart buildings

Wesley Holt

Ph.D. Student

Information field theory

Shrenik Vijaykumar Zinage

Ph.D. Student

Emissions modeling

szinage@purdue.edu

Google Scholar

ResearchGate

GitHub

Maxwell Bolt

Ph.D. Student

Emissions modeling

Rohan Dekate

Ph.D. Student

Operator learning

For a list of former members, please visit the PSL website.

How to join the group?

We are continuously looking for qualified people to join the group. If you are interested in working with us, please send me an email with your CV and a brief description of your research interests. I will get back to you as soon as possible.

About this website

This website was made in plain html with the help of ChatGPT. If you want to have fun, you can see the log of our conversation here. It was last updated on September 17, 2024.