Jinhua Lyu

I am a second-year PhD candidate in the Department of Industrial Engineering and Management Science (IEMS) at Northwestern University, fortunate to be advised by Prof. Naichen Shi.

I received my M.S. degree in Operations Research from the University of Texas at Austin, where I was fortunate to be advised by Prof. Jonathan F. Bard. Before that, I earned my bachelor's degree from Nankai University.

My research develops optimization and statistical methodologies for scientific and engineering problems, with a current focus on generative modeling of structured tensor data and physical dynamics.

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Research

We construct data-dependent tensor primitives by Tucker decomposition with orthogonal Procrustes alignment to medoid anchors, yielding compact, directly decodable representations of high-dimensional fields without any pretrained autoencoder. Diffusion models trained on these primitives achieve strong unconditional and conditional generation on images, videos, and PDE solutions, with compression ratios from 3.9x to 210x.

Mean-Field Variational Inference (MFVI) struggles on hierarchical models where the number of latent variables grows with the data. We propose a mini-batch MFVI and a primal-dual algorithm, PD-VI, together with a block-preconditioned variant, P²D-VI, that use an augmented Lagrangian to jointly update global and local parameters while adapting to heterogeneous loss geometries. On a spatial transcriptomics domain detection task, P²D-VI segments transcriptomic profiles across over 150,000 locations in under 6 seconds.

Inspired by this template.