Zhikai Wu | Yuanpei College, Peking University

About Me

I’m a forth-year undergraduate student at Yuanpei College, Peking University. From August 2024 to September 2025, I worked as a research assistant at Yale University advised by Prof. Lu Lu and Prof. David van Dijk, completing two research projects. Since September 2025, I have been working online with Prof. Paris Perdikaris at the University of Pennsylvania, leading a self-initiated research project.

My research interests lie in the partial differential equations (PDE) and their data-driven solution operator.

News

[Feb 2026] Admitted by Courant Institute, NYU as a PhD student in Data Science, advised by Prof. Zongyi Li.
[Nov 2025] GRE Mathematics Subject Test: 930/990 (higher than 94% of test takers).
[Sep 2025] Posted “GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometries” on arXiv.
[Sep 2025] Joined the University of Pennsylvania as an online research assistant (advised by Prof. Paris Perdikaris).

Selected Publications

Time-Adaptive Operator Learning via Neural Taylor Expansion

We propose Time-Adaptive Transformer with Neural Taylor Expansion (TANTE), a novel operator-learning framework that produces continuous-time predictions for with adaptive step sizes. We demonstrate the effectiveness of TANTE across four challenging PDE benchmarks, achieving superior accuracy and adaptability compared to fixed-step baselines, delivering accuracy gains of 60-80% and speed-ups of 30-40% at inference time. — Under Review

Paper Code

Complete Publication List

(*Equal Contribution)

Filter by Research Area

# Adaptive Step Size # Data-driven # Inverse Problems # JAX # Microbial Community # PDEs # PyTorch # Signal processing # Taylor Expansion

2025

TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansion

Zhikai Wu, Sifan Wang, Shiyang Zhang, Sizhuang He, Min Zhu and 3 more authors

Under Review

Abstract BibTex Paper Code

# PyTorch # Data-driven # Adaptive Step Size # PDEs # Taylor Expansion
Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step sizes during rollout, which limits their ability to adapt to varying temporal complexity and often leads to error accumulation. Here, we propose the Time-Adaptive Transformer with Neural Taylor Expansion (TANTE), a novel operator-learning framework that produces continuous-time predictions with adaptive step sizes. TANTE predicts future states by performing a Taylor expansion at the current state, where neural networks learn both the higher-order temporal derivatives and the local radius of convergence. This allows the model to dynamically adjust its rollout based on the local behavior of the solution, thereby reducing cumulative error and improving computational efficiency. We demonstrate the effectiveness of TANTE across a wide range of PDE benchmarks, achieving superior accuracy and adaptability compared to fixed-step baselines, delivering accuracy gains of 60-80% and speed-ups of 30-40% at inference time. The code is publicly available at https://github.com/zwu88/TANTE for transparency and reproducibility.
GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometries

Sifan Wang^*, Zhikai Wu^*, David van Dijk, and Lu Lu

Under Review

Abstract BibTex Paper

# JAX # Data-driven # Inverse Problems # PDEs
Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical PDE-constrained optimization methods are accurate and robust but are computationally expensive, especially when repeated posterior sampling is required. Learning-based approaches improve efficiency and scalability, yet most are designed for regular domains or focus primarily on forward modeling. To fill this gap, we introduce GeoFunFlow, a geometric diffusion framework for inverse problems on complex geometries. GeoFunflow combines a novel geometric functional autoencoder (GeoFAE) and a latent diffusion model trained via rectified flow. GeoFAE employs a Perceiver module to process unstructured meshes of varying sizes and produces continuous reconstructions of solution fields, while the diffusion model enables posterior sampling from sparse and noisy data. Across five standard benchmarks, GeoFunflow achieves state-of-the-art reconstruction accuracy over complex geometries, provides calibrated uncertainty quantification, and delivers efficient inference compared to operator-learning and diffusion baselines.

2024

Predicting Microbial Community Productivity Based-On Genomic Sequences with Graph Neural Network

Jiaheng Hou, Peter X Geng, Zhikai Wu, Wenlin Fan, and Huaiqiu Zhu

2024 17th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics

Abstract BibTex Paper

# Signal processing # Microbial Community
Artificial microbial community design has gained increasing attention due to its economic and environmental benefits. However, it is challenging considering the complex microbial interactions and emergent properties arising from metabolic networks. Although flux balance analysis (FBA), based on genome-scale metabolic models (GEMs), is a well-known approach for simulating community phenotypes, its inefficiency in handling communities with a large number of functional genes limits its utility. In this paper, we introduce a novel graph neural network model that incorporates growth-coupling effects to predict the productivity of microbial communities, which is impractical for prior techniques. Utilizing 83 high-quality bacterial GEMs, we trained and tested our model on a large number of bacterial communities containing two or three strains, each undergoing a random genetic modification (either knock-outs or knock-ins) within the community GEM. Our model demonstrates high concordance with FBA, achieving an average area under the curve (AUC) of 0.98, and a F1 score of 0.82. Notably, it operates approximately 6,415 times faster than FBA. Our model indicates that graph-based machine learning algorithms can significantly accelerate productivity prediction and hold potential to advance microbial community design, thereby guiding microbial engineering strategies.

Timeline

[2025/09] Invited seminar at the University of Pennsylvania on my research (host: Prof. Paris Perdikaris).
[2025/08] Invited talk at Yale University on my paper (host: Prof. Lu Lu).
[2025/05] Posted “TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansion” on arXiv.
[2025/04] Invited online talk at Yale University on my paper (host: Prof. Lu Lu).
[2024/08] Presentation at Yale University on my research proposal (host: Prof. David van Dijk).
[2024/08] Joined Yale University as a research assistant (advised by Prof. Lu Lu and Prof. David van Dijk).
[2024/07] Attended the Summer Programme on International Affairs at the Geneva Graduate Institute (Geneva, Switzerland).

Services

Journal Reviewer:
- Engineering with Computers
- Computational and Applied Mathematics (COAM)
- Journal of Medical Internet Research (JMIR)

Apart from research

To learn more about my musical work, please visit my Music Page.

Conductor: Lead the regular rehearsals, coordinate semiannual auditions, conducted and coordinated eight concerts.
- [2022-Present] Orchestra Conductor: Symphony Orchestra of Student Strings Association, Peking University
- [2024-Present] Chorus Conductor: Yuanpei Acoustic Chamber Choir, Peking University
- [2024-Present] Chorus Conductor: Retirees Choir, Peking University ($40/hr earned)
- [2024-2025] President: Student Strings Association, Peking University
- [2023-2024] Director: Performance Department of Student Strings Association, Peking University
Pianist: Taught piano lessons, interviewed semiannual auditions, and performed as a pianist in four concerts.
- [2023-2024] Director: Performance Department of Piano Association, Peking University
- [Fall 2023] Piano Instructor: Advanced Piano Lessons of Piano Association, Peking University
- [2022-Present] Member: Performance Department of Piano Association, Peking University

I also enjoy traveling and exploring different parts of the world. Here are some of the places I’ve visited (outside of China and the U.S.):

New Zealand: Queenstown, Auckland (self-driving)
Australia: Sydney, Melbourne
Turkey: Istanbul
Singapore
France: Lyon, Paris
Switzerland: Geneva, Nyon, Bern, Lausanne, Interlaken, Zurich, Lucerne

Feel free to reach out if you’d like travel tips for any of these cities, or have suggestions for my future trips. Travel posts are coming soon!