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

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

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.

- 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:

- 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)

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

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.

Professor of Mechanical Engineering

Purdue University

ibilion@purdue.edu

Postdoctoral Researcher

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

Postdoctoral Researcher

Physics-informed, information field theory

Postdoctoral Researcher

Physics-informed, information field theory for dynamical systems

Postdoctoral Researcher

Superresolution of 4D flow MRI using information field theory

hans1@purdue.edu

Ph.D. Student

Purdue University

beltranp@purdue.edu

Electric machine design optimization using physics informed neural networks

Ph.D. Student

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

Ph.D. Student

Digital twins for smart buildings

Ph.D. Student

Information field theory

Ph.D. Student

Emissions modeling

szinage@purdue.edu

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.