Zhuoyuan Li

Zhuoyuan Li

Research Fellow, National University of Singapore

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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

Pages

Posts

Future Blog Post

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Blog Post number 4

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Blog Post number 3

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Blog Post number 2

less than 1 minute read

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Blog Post number 1

less than 1 minute read

Published:

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portfolio

publications

Learning to simulate partially known spatio-temporal dynamics with trainable difference operators

Published in arXiv, 2023

Recently, using neural networks to simulate spatio-temporal dynamics has received a lot of attention. However, most existing methods adopt pure data-driven black-box models, which have limited accuracy and interpretability. By combining trainable difference operators with black-box models, we propose a new hybrid architecture explicitly embedded with partial prior knowledge of the underlying PDEs named PDE-Net++. Furthermore, we introduce two distinct options called the trainable flipping difference layer (TFDL) and the trainable dynamic difference layer (TDDL) for the difference operators. Numerous numerical experiments have demonstrated that PDE-Net++ has superior prediction accuracy and better extrapolation performance than black-box models.

Recommended citation: Huang, X., Li, Z., Liu, H., Wang, Z., Zhou, H., Dong, B., & Hua, B. (2023). Learning to simulate partially known spatio-temporal dynamics with trainable difference operators. arXiv preprint arXiv:2307.14395. https://arxiv.org/pdf/2307.14395.pdf

Latent assimilation with implicit neural representations for unknown dynamics

Published in Journal of Computational Physics, 2024

Data assimilation is crucial in a wide range of applications, but it often faces challenges such as high computational costs due to data dimensionality and incomplete understanding of underlying mechanisms. To address these challenges, this study presents a novel assimilation framework, termed Latent Assimilation with Implicit Neural Representations (LAINR). By introducing Spherical Implicit Neural Representations (SINR) along with a data-driven uncertainty estimator of the trained neural networks, LAINR enhances efficiency in assimilation process. Experimental results indicate that LAINR holds certain advantage over existing methods based on AutoEncoders, both in terms of accuracy and efficiency.

Recommended citation: Li, Z., Dong, B., & Zhang, P. (2024). Latent assimilation with implicit neural representations for unknown dynamics. Journal of Computational Physics, page 112953. https://doi.org/10.1016/j.jcp.2024.112953

State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics

Published in Journal of Computational Physics, 2025

Data assimilation has become a crucial technique aiming to combine physical models with observational data to estimate state variables. Traditional assimilation algorithms often face challenges of high nonlinearity brought by both the physical and observational models. In this work, we propose a novel data-driven assimilation algorithm based on generative models to address such concerns. Our State-Observation Augmented Diffusion (SOAD) model is designed to handle nonlinear physical and observational models more effectively. The marginal posterior associated with SOAD has been derived and then proved to match the real posterior under mild assumptions, which shows theoretical superiority over previous score-based assimilation works. Experimental results also indicate that our SOAD model may offer improved accuracy over existing data-driven methods.

Recommended citation: Li, Z., Dong, B., & Zhang, P. (2025). State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics. Journal of Computational Physics, page 114240. https://doi.org/10.1016/j.jcp.2025.114240

Fluorescent protein-based ticker tapes for multiplexed recordings of transcriptional histories in single cells in culture and in vivo

Published in bioRxiv, 2025

Recording and imaging of promoter activities in real time is critical for deciphering cellular states and dynamic signaling crosstalk, but technologies capable of simultaneously capturing multiple transient events in living cells are lacking. Here, we custom-design fluorescent protein-based ticker tapes (FPTT) for multiplexed and longitudinal recording of physiological activities in single cells. FPTT integrates multi-spectral monomeric fluorescent proteins with self-assembling protein fibers, enabling massively parallel analysis of signaling dynamics under varying cellular conditions. Using FPTT, we were able to log dose-dependent and reversible transcriptional histories of endogenous cFos signaling in primary hippocampus neurons at a 3-hour temporal resolution via biological timestamps and an extended recording time of over 8 days. Furthermore, we expanded the imaging toolset by engineering genetically encoded FPTT variants for human NFκB, JAK/STAT3, mTOR, NFAT and cAMP signaling, allowing for the quantification of potential crosstalk between cFos and NFκB pathways in neurons, multiplexed recording of STAT3- and cAMP-specific promoters during drug-induced liver injury in mice, as well as simultaneous analysis of up to four major signaling pathways involved in experimental T-cell activation. This platform advances single-cell analysis by providing a versatile tool to investigate transcriptional histories and signaling interplay across diverse biological contexts, with broad applications in developmental biology and disease modeling.

Recommended citation: Wang, R., Jiang, J., Li, Z., Liu, T., Wang, Y., Xie, M., & Piatkevich, K. D. (2025). Fluorescent protein-based ticker tapes for multiplexed recordings of transcriptional histories in single cells in culture and in vivo. bioRxiv 2025.09.08.675004. https://www.biorxiv.org/content/10.1101/2025.09.08.675004v1

Spend Wisely: Maximizing Post-Training Gains in Iterative Synthetic Data Bootstrapping

Published in Advances in Neural Information Processing Systems, 2025

Modern foundation models often undergo iterative “bootstrapping” in their post-training phase: a model generates synthetic data, an external verifier filters out low-quality samples, and the high-quality subset is used for further fine-tuning. Over multiple iterations, the model’s performance improves—raising a crucial question: how should the total budget on generation and training be allocated across iterations to maximize final performance? In this work, we develop a theoretical framework to analyze budget allocation strategies. Specifically, we show that constant policies fail to converge with high probability, while increasing policies—particularly exponential growth policies—exhibit significant theoretical advantages. Experiments on image denoising with diffusion probabilistic models and math reasoning with large language models show that both exponential and polynomial growth policies consistently outperform constant approaches, with exponential policies often providing more stable performance.

Recommended citation: Yang, P., Feng, Y., Chen, Z., Wu, Y., & Li, Z. (2025). Spend Wisely: Maximizing Post-Training Gains in Iterative Synthetic Data Bootstrapping. in Advances in Neural Information Processing Systems, 38. https://arxiv.org/pdf/2501.18962

In-context modeling as a retrain-free paradigm for foundation models in computational science

Published in arxiv, 2026

Building models that generalize across physical systems without retraining remains a central challenge in computational science. Here we introduce In-Context Modeling (ICM), a retrain-free paradigm that infers physical relationships directly from observational fields. Rather than encoding system-specific behavior in fixed parameters, ICM assimilates measurements as physical context and performs inference through a single forward pass. Trained in a physics-informed, label-free manner using governing equations, a single model generalizes across unseen materials, geometries, and loading conditions. Demonstrated on hyperelasticity, ICM integrates with finite-element simulations and is validated using experimental full-field measurements. Moreover, performance improves with increasing data diversity and computational budget, exhibiting favorable scaling behavior analogous to foundation models. By recasting physical modeling as in-context inference, this work establishes a transferable paradigm for retrain-free scientific learning and a foundation for scalable modeling across computational science.

Recommended citation: Li, L., Li, Z., Li, S., Zhan, K., Gao, H., Chen, C., & Yang, L. (2026). In-context modeling as a retrain-free paradigm for foundation models in computational science. arXiv preprint arXiv:2604.23098. https://arxiv.org/pdf/2604.23098

Hypothesis-driven construction of mesoscopic dynamics

Published in arxiv, 2026

Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class. Building upon a generalized Onsager principle, we introduce a unified framework encompassing both dissipative and conservative mesoscopic dynamics. We establish uniform and a priori theoretical guarantees, including global well-posedness, asymptotic stability, unique factorization identifiability, and discrete energy dissipation, applicable to all spatio-temporal evolution equations within this hypothesis class prior to all learning stages. Data from each problem instance is then used to guide the identification of members within our hypothesis class, giving rise to accurate, robust and interpretable dynamical models. We empirically validate this framework on both data from continuum PDE models as a check, and on data arising from microscopic chain models for which exact meso-scale models are unknown. The proposed approach not only acts as an effective dynamics learner, but also offers vital interpretable diagnostics of the underlying physics.

Recommended citation: Li, Z., Zhu, A., & Li. Q. (2026). Hypothesis-driven construction of mesoscopic dynamics. arXiv preprint arXiv:2605.16211. https://arxiv.org/pdf/2605.16211

talks

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

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Teaching experience 2

Workshop, University 1, Department, 2015

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