THEME 2- Partial Differential Equations

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Session DescriptionThe physical processes characterizing biological systems, from the cell to the tissue and organ levels, is generally captured through partial differential equations (PDEs). The interactions between the different scales in these systems is complex with many unknown parameters, making it challenging to model them in a multi-dimensional parametric space (in addition to 3D physical space plus time), requiring also uncertainty quantification methods. Moreover, modeling these systems depends crucially on the data available, and new multi-modality data collection methods will play a key role in the effective use of PDE modeling in multiscale biological systems. Hence, physics-informed machine learning can play a key role in levering any multi-fidelity or multi-modality data with any known physics, and these data can be exploited to discover the missing physics. 

This session will start with three 15-minutes keynote lectures from experts in machine learning, uncertainty quantification, and multiscale modeling of biological systems. Dr. George Karniadakis will also provide some remarks in a 15-minute presentation before an interactive panel discussion with the audience for the remainder 30 minutes of the session. 

 

Keynote Speakers

Dr. Chinmay Hegde is an an Assistant Professor in the Electrical and Computer Engineering Department at Iowa State University. His research group is interested broadly in problems related to data processing and machine learning. His group focuses on developing fast and robust algorithms for diverse problems in data sensing and inference.

Keynote title: Solving PDEs using Conditional Generative Models

 

Dr. Ilias Bilionis is an Assistant Professor of Mechanical Engineering at Purdue University and his research is motivated by energy and material science applications and it focuses on the development of generic methodologies for design and optimization under uncertainty, reliability analysis, model calibration and learning models out of data.

Keynote title: Physics-informed Machine Learning: A Very Gentle Introduction

 

Dr. Eric Mjolsness is a Professor in the Departments of Computer Science and Mathematics at University of California Irvine. His group is focused on mathemical AI/ML for multiscale sicence, with a strong emphasis on biology. Mathematical AI is Artificial Intelligence via high-level symbolic representations (such as computer algebra) of applied mathematical analysis, geometry, algebra, etc.; and ML is mathematical machine learning.

Keynote title: Learning PDE model reductions/moment closures of stochastic reaction/diffusion dynamics

 

Moderators:

Dr. Adrian Buganza Tepole is an Assistant Professor of Mechanical Engineering at Purdue University. His group studies the interplay between mechanics and biology. Utilizing computational methods for solution of partial differential equations, combined with machine learning tools and data from experiments, his group seeks to understand the fundamental mechanisms of living tissue adaptaion.

Dr. George Karniadakis is a Professor in Applied Mathematics at Brown University. His current research interests are on machine learning for scientific computing, that is how to solve and discover new PDEs via deep learning, hence removing the tyranny of grids and using gappy data only. His broad research interests focus on stochastic multiscale mathematics and modeling of physical and biological systems. 

 

Questions for the audience:

  • How to leverage machine learning to model biological systems with high-dimensional inputs at multiple scales? ML applied to change of scale mappings 
  • How can we solve ill-posed inverse problems for parameter estimation or system identification? Regularization
  • How can we remove the tyranny of grid generations of conventional methods? Unification of mesh and particle methods
  • How can we couple conventional physics (mass and momentum balance) with stochastic reaction-diffusion over time for living system adaptation?
  • How can fuse different types of data?
  • How to ensure reproducibility of results and creation of benchmarks?
  • How to separate the biophysical (model + data) from the uncertainty of the machine learning method?
  • How to decide which machine learning algorithms will be best suited for particular problems?
  • How to fuse images and point measurements? 
  • How to quantify errors and total uncertainty (NN, parametric, modeling, data)?
  • Symbolic auto-generation of bespoke (problem/biophysical-model-specific) ML data models and algorithms
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