About the Authors

Hung-Yu Chang

Affiliation Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America

Xuejin Li

Xuejin_Li@brown.edu (XL); George_Karniadakis@brown.edu (GEK)

Affiliation Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America

He Li

Affiliation Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America

George Em Karniadakis

Xuejin_Li@brown.edu (XL); George_Karniadakis@brown.edu (GEK)

Affiliation Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: HYC XL HL GEK. Performed the experiments: HYC XL HL. Analyzed the data: HYC XL HL GEK. Contributed reagents/materials/analysis tools: HYC XL HL GEK. Wrote the paper: HYC XL HL GEK.