Applied Mathematics for Trustworthy AI and Scientific Discovery
I am a Postdoctoral Scholar at Stanford University and SLAC National Accelerator Laboratory, where I work with Professor Thomas Devereaux on the mathematical foundations of artificial intelligence for computational quantum physics. My current research focuses on neural quantum states and trustworthy AI methods for scalable forward and inverse problems in quantum many-body systems.
More broadly, I develop mathematical frameworks for machine learning using optimal transport, information theory, probability, stochastic dynamics, optimization, and statistical inference. My goal is to translate mathematical structure into scalable algorithms with interpretable behavior and verifiable guarantees, particularly for AI for science and other high-stakes applications.
Before joining Stanford and SLAC, I was a Postdoctoral Scholar in Mathematics at the University of California, Davis, working with Professor Thomas Strohmer on trustworthy machine learning. I received my Ph.D. in Applied Mathematics from UC Davis in 2024; my dissertation studied fairness in machine learning through the lens of optimal transport.
Recent news
- September 2026: On the (In)Compatibility between Group Fairness and Individual Fairness was accepted for publication in the SIAM Journal on Mathematics of Data Science.
- August 2026: Our paper, Multi-resolution enhancement for full-spectrum neural representations, was published in Nature Machine Intelligence.
- July 2026: I joined Stanford University and SLAC National Accelerator Laboratory to work on mathematical foundations of AI for computational quantum physics.
Research
My research asks how geometry, information, and dynamics can make modern AI systems more reliable and scientifically useful. My current program has three closely connected themes:
- AI for science and computational quantum physics. I study the mathematical foundations of neural quantum states, including their expressivity, optimization, sampling, and reliability, and develop trustworthy AI methods for forward and inverse problems in quantum many-body systems.
- Optimal transport and information theory. I use the geometry of probability distributions and measures of information to formulate learning objectives, characterize fundamental trade-offs, and design algorithms with provable guarantees.
- Trustworthy machine learning. I develop auditable methods for fairness, machine unlearning, privacy, robustness, uncertainty quantification, and reliable decision-making.
Across these areas, I work from mathematical principles to implementable algorithms and evaluate the resulting methods in collaboration with domain scientists.
Learn more about my research →
Selected publications
Shizhou Xu and Thomas Strohmer.
On the (In)Compatibility between Group Fairness and Individual Fairness.
Accepted, SIAM Journal on Mathematics of Data Science, 2026.Yuan Ni, Zhantao Chen, Shizhou Xu, et al.
Multi-resolution enhancement for full-spectrum neural representations.
Nature Machine Intelligence, 2026.Shizhou Xu and Thomas Strohmer.
Fair Data Representation for Machine Learning at the Pareto Frontier.
Journal of Machine Learning Research, 24 (2023), 1–63.Shizhou Xu and Thomas Strohmer.
WHOMP: Optimizing Randomized Controlled Trials via Wasserstein Homogeneity.
CPAL Spotlight, ICLR Workshop, 2025.Shizhou Xu and Thomas Strohmer.
Machine Unlearning via Information Theoretic Regularization.
Preprint, 2025; revised 2026.
Selected research impact
- Fairness and AI governance: My work on fair data representation is cited as a reference in the Alan Turing Institute–Mastercard report on fairness in financial-transaction machine-learning models.
- Biomedical experimentation: My WHOMP method and accompanying software were adopted by Quantum Leap Healthcare Collaborative to reduce accidental bias in a clinical trial involving approximately 2,000 cancer patients.
- Machine unlearning: My collaborators and I have a pending patent application for marginal-information regularization for selective forgetting in large language models (LLMs).
Teaching and professional service
- Teaching: Instructor of record for Real Analysis at UC Davis; teaching assistant and recitation leader for courses in vector analysis, linear algebra, calculus, and mathematics for economics.
- Community building: Co-organizer of the Mathematics of Data and Decisions Seminar at UC Davis.
- Reviewing: Reviewer for ICML, NeurIPS, ICLR, Physical Review X, and the SIAM Journal on Mathematics of Data Science.
Contact
Email: shzxu@stanford.edu
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