Ph.D. (2020.09 - Present), Statistics and Applied Probability, University of California, Santa Barbara
Advisor: Mengyang Gu (Homepage)
MS (2018.08 - 2020.05), Statistics, University of Southern California
BS (2016.01 - 2019.12), Applied and Computational Mathematics, University of Southern California
Minor: Applied Analytics
Machine Learning/Gaussian Process/Kalman Filter/Dimension Reduction
Xinyi Fang*, Mengyang Gu* (*Equal Contribution)
Accepted in Biometrika | arXiv link | GitHub code
Summary: We introduce the inverse Kalman filter (IKF), which enables accurate matrix-vector multiplication with linear computational cost for covariance matrices from dynamic linear models. Integrating IKF with the conjugate gradient algorithm allows efficient computation of predictive distributions in Gaussian processes. Applications include nonparametric estimation of particle interaction functions and predicting incomplete lattices of correlated data.
Universal Phase Identification of Diblock Copolymers from Automated Statistical Learning
Xinyi Fang*, Elizabeth A. Murphy*, Phillip Kohl, Youli Li, Craig J. Hawker, Christopher M. Bates, Mengyang Gu (*Equal Contribution)
Journal of Polymer Science (2025) | ChemRxiv link | GitHub code
Summary: By combining automated polymer processing and physics-informed machine learning, we developed a high-throughput method that identifies block copolymer structures with 95% accuracy. This universal approach analyzes X-ray scattering patterns independently of chemical composition, enabling rapid phase identification while requiring expert review of only 15% of samples to achieve near-perfect accuracy.
Data-driven model construction for anisotropic dynamics of active matter
Mengyang Gu, Xinyi Fang, Yimin Luo
PRX Life (2023) | arXiv link | GitHub code | News | Yale Daily News
Summary: We introduce a hybrid approach that combines statistical learning techniques with physics models to comprehensively explain the temporal progression of cell alignment on molecularly aligned substrates. Our model, which considers cell-cell interactions and substrate influences, quantitatively reproduces key system-level parameters, making it a valuable tool for understanding similar systems of active matter.
Yimin Luo, Mengyang Gu, Minwook Park, Xinyi Fang, Younghoon Kwon, Juan Manuel Urueña, Javier Read de Alaniz, Matthew E. Helgeson, M. Cristina Marchetti, Megan T. Valentine
Journal of the Royal Society Interface (2023) | arXiv link
Reliable emulation of complex functionals by active learning with error control
Xinyi Fang*, Mengyang Gu*, Jianzhong Wu (*Equal Contribution)
The Journal of Chemical Physics (2022) | arXiv link | GitHub code
Summary: This paper introduces ALEC, an active learning with error control algorithm for modeling complex high-dimensional functionals with high accuracy. Through emulation of classical density functional theory (cDFT) calculations, ALEC demonstrates its superior accuracy over traditional "space-filling" approaches and other active learning methods, owing to its controllable predictive error and automatic features.
Mengyang Gu, Xubo Liu, Xinyi Fang, Sui Tang
New England Journal of Statistics in Data Science (2022) | arXiv link | GitHub code
Summary: This work presents an innovative approach for modeling correlated data, such as spatio-temporal or functional observations. By leveraging the connection between state space models and Gaussian processes with Matérn covariance, we reduce computational costs through sparse representation of the inverse covariance matrix of latent variables and employ conjugate gradient techniques to enhance predictive accuracy with extensive datasets.
Pan, R., Fang, X., Azizzadenesheli, K., Liu-Schiaffini, M., Gu, M., & Wu, J. (2025). Neural Operators for Forward and Inverse Potential-Density Mappings in Classical Density Functional Theory. arXiv preprint arXiv:2506.06623.
