Dr. Ziqian Li
Email • PhD in Mathematics, Jilin University
Optimal control in fluid mixing, neural ODEs, deep learning solving PDEs
PhD Student
Supervisor: Enrique Zuazua
Room 03.319 | FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship
Friedrich-Alexander-Universität Erlangen-Nürnberg
Naturwissenschaftliche Fakultät. Department Mathematik
Research Gate | ORCID | Google Scholar
Personal site | LinkedIn
Hi! My name is Ziqian Li, and I am a doctoral student at FAU DCN-AvH, the Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship under the supervision of Prof. Enrique Zuazua at Friedrich-Alexander-Universität Erlangen-Nürnberg, Bavaria (Germany).
I obtained my first PhD degree in mathematics at Jilin University (China) under the supervision of Prof. Tao Tang and Prof. Ran Zhang.
My research directions are optimal control in fluid mixing, neural ODEs and deep learning solving partial differential equations.
• PhD Thesis: Neural Ordinary Differential Equations: Approximation Theory and Its Applications in Operator Learning (June 2026)
See more: News
Research interests
My research interests include
• Optimal control in fluid mixing,
• Neural ODEs,
• Deep learning solving partial differential equations,
Projects
• CoDeFeL. Control for Deep and Federated Learning (2024 – now)
• DTN ModConFlex. Modelling and control of flexible structures interacting with fluids (2024 – now)
Awards
• Outstanding Poster Award: Approximation Theory and applications of semi-autonomous Neural ODEs
ICBS 2025 – International Congress of Basic Science 2025 (Beijing, China)
News / Initiatives
Poster at the Mathematics for Machine Learning in Burgundy: Approximation Theory and Applications of Semi-Autonomous Neural ODEs (slides). Dijon, France
Authors: Ziqian Li
Date: June 16, 2026
Talk at EZ65: Control, PDEs and Machine Learning workshop: Deep Neural ODE Operator Networks for PDEs (slides)
Authors: Ziqian Li
Date: June 11, 2026
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FAU DCN-AvH Jr. Seminar: Approximation of dynamical systems via semi-autonomous NODEs
Authors: Ziqian Li, Enrique Zuazua
Date: April 29, 2026
Neural ODEs: Approximation Theory and Operator Learning | slides
Authors: Ziqian Li
Date: March 02, 2026
Deep Neural ODE Operator Networks for PDEs | Slides. FAU MoD/GMU workshop: The Mathematics of Scientific Machine Learning and Digital Twins.
Authors: Ziqian Li
Date: November 20, 2025
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Approximation Theory and applications of semi-autonomous Neural ODEs
Authors: Ziqian Li, Lorenzo Liverani, Enrique Zuazua, Kang Liu
Date: July 18, 2025
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Greedy Algorithm for Neural Networks for Indefinite Elliptic Problems
Authors: Ziqian Li
Date: March 24, 2025
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Publications
2026
- , , , :
A Structure-Preserving Numerical Scheme for Optimal Control and Design of Mixing in Incompressible Flows
(2026)
BibTeX: Download - , , , :
Universal Approximation of Dynamical Systems by Semiautonomous Neural ODEs and Applications
In: SIAM Journal on Numerical Analysis 64 (2026), p. 193 - 223
ISSN: 0036-1429
DOI: 10.1137/24M1679690
BibTeX: Download - , , , , :
Deep Neural ODE Operator Networks for PDEs
In: Mathematical Models & Methods in Applied Sciences 36 (2026), p. 1739-1782
ISSN: 0218-2025
DOI: 10.1142/S0218202526420054
URL: https://www.worldscientific.com/doi/abs/10.1142/S0218202526420054
BibTeX: Download - , :
Hamiltonian Interface Dynamics for Reduced-Order Optimization of Incompressible Mixing
(2026)
DOI: 10.48550/arXiv.2605.04688
URL: https://arxiv.org/abs/2605.04688
BibTeX: Download
2025
- , , , :
Greedy Algorithm for Neural Networks for Indefinite Elliptic Problems
In: Journal of Scientific Computing (2025)
ISSN: 0885-7474
URL: https://link.springer.com/article/10.1007/s10915-025-03021-w#Bib1
BibTeX: Download
