About the Authors

Sheng Zhang

Contributed equally to this work with: Sheng Zhang, Joan Ponce, Zhen Zhang

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing

Affiliation Department of Mathematics, Purdue University, West Lafayette, Indiana, United States

Joan Ponce

Contributed equally to this work with: Sheng Zhang, Joan Ponce, Zhen Zhang

Roles Conceptualization, Investigation, Methodology, Project administration, Resources, Writing – original draft, Writing – review & editing

Affiliation Department of Mathematics, Purdue University, West Lafayette, Indiana, United States

Zhen Zhang

Contributed equally to this work with: Sheng Zhang, Joan Ponce, Zhen Zhang

Roles Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing

Affiliation Division of Applied Mathematics and School of Engineering, Brown University, Providence, Rhode Island, United States

Guang Lin

Roles Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Writing – review & editing

guanglin@purdue.edu

Affiliations Department of Mathematics, Purdue University, West Lafayette, Indiana, United States, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, United States

George Karniadakis

Roles Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Writing – review & editing

Affiliation Division of Applied Mathematics and School of Engineering, Brown University, Providence, Rhode Island, United States

Competing Interests

The authors have declared that no competing interests exist.