Hello! My name is Anqiao Ouyang (Auyeung). I'm a researcher in collaboration with the Advanced Data Assimilation Lab at San Diego State University, working at the intersection of computer science and mathematics. My research broadly explores machine and deep learning for scientific computing, with interests spanning numerical methods, structure-aware modeling, and data-driven approaches to complex systems. Much of my work is motivated by questions where geometry, dynamics, and computation naturally meet.
Outside of lab and project work, mathematics is a long-standing personal interest. I am particularly drawn to mathematical analysis and topology—not so much for specific results, but for the way they shape how one thinks about limits, continuity, structure, and invariance.
This is my personal blog. I share notes, mini-lectures, and project updates across mathematics and computer science, mixing theory with computation and the occasional essay, in a space meant to be thoughtful, informal, and unapologetically curious.
Mathematics Community
Mx. Ouyang's Drama Room Info (Groups)
My interest in computer science started in middle school, where operating systems and compilation principles were what I found most compelling. Over time, I crossed paths with people far more capable than me, and learned more from that than from anything else. Since late 2022, I've been active in GDG, engaging with developer communities around the world, and the experience has shaped me in ways I didn't anticipate.
I study languages mostly for the pleasure of it. I began with Japanese, self-taught; then German at fourteen; and now French at a Canadian high school, where I've had the rare fortune of truly excellent teachers. I care about languages not just as tools, but as carriers of culture. For reasons I've never felt the need to fully explain, le français est devenu ma langue préférée.
Mathematics is embedded in how I think. My academic work, professional pursuits, and even my everyday reasoning all run on it. One of my colleagues once said to me that "the ceiling of one's mathematics determines the ceiling of one's science."
Reading has been a constant in my life for as long as I can remember. It sharpens my thinking, broadens my frame of reference, and has long served as my most reliable refuge. Some people party on weekends. I turn pages.
I began studying painting around 2016, with a focus on figure drawing. Over the years, it has become less a hobby and more a ritual: a way to slow down when everything else feels relentless. I make no claims to being an artist, but I find deep satisfaction in the process, and I keep working toward pieces I'm genuinely proud of.
Without coffee, I'm basically a sophisticated potato.
Dark roast, black—no milk, no sugar. I like my coffee to taste like coffee.
San Diego State University
Researcher
American Physical Society
Graduate Member
American Mathematical Society
Affiliate Member
A framework for exact homology maintenance on evolving simplicial complexes. It maintains homology without global rebuilds by combining an initial discrete-Morse reduction with modular, locality-bounded updates. By compressing the input to a critical cell complex chain-homotopy equivalent to the original; subsequent edits trigger updates restricted to the affected critical columns of the reduced boundary operators over a chosen coefficient ring. A column-oriented sparse representation with a pivot-ownership map confines elimination and enables fast, localized reductions, while topology-aware gating can short-circuit linear algebra entirely when invariants are decidable combinatorially. Periodic recompression controls drift and preserves compactness of the reduced complex. The result is an exact, amortized-efficient alternative to global recomputation that slots into existing topology pipelines, turning costly boundary-matrix reconstructions into fast, local homology maintenance through continuous edits.
A general representation for homogeneous and spatially stationary flows that combines invertibility with frequency-domain priors: in the Fourier domain, high-dimensional fields are compressed into low-dimensional latent variables while preserving the energy spectrum and coherent structures, and an invertible mapping reconstructs the original field. The representation serves as a stable basis for reduced-order models (ROM) and supports compression, fast reconstruction, visualization, forecasting, and control; frequency-domain modeling also handles translations and periodic boundaries naturally. Compared to conventional convolutional autoencoders, the approach is simpler with fewer parameters, offers higher fidelity on nonlinear, high-frequency signals, and achieves substantial gains in reconstruction accuracy.
This is my WeChat Official account. I post short notes and longer essays irregularly,
along with China-only updates such as offline meetups and community activities.
Note: purely academic blog posts are mirrored here at Articles
as PDFs.
Notes and mini-lectures that emphasize rigor and computation side by side.
From theory to systems, focusing on reproducible workflows and practical design.
Short essays connecting technical work with human concerns and ideas.
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Posted by: Anqiao Ouyang, March 15, 2021
Contact information: [email protected]
Pronouns: Any (Biological gender: female)