I’m a researcher at Sandia National Laboratories in Albuquerque, working on scientific machine learning, numerical PDEs, and deep learning theory.
Previously: College senior at Cornell University. Second Third year Fourth year graduate student at Brown University (I was apparently too busy first year of grad school to update this page). Postdoc at Brown University. I have survived the academic pipeline and emerged in the desert.
I did my PhD in applied mathematics at Brown University as an NDSEG Fellow, advised by Mark Ainsworth. My thesis was on preconditioning for high-order finite element methods. Before that, I graduated from Cornell in 2015 with a double major in mathematics and economics and a CS minor.
Research
These days my work sits at the intersection of numerical analysis, scientific computing, and machine learning. On the numerical side, I’ve worked on preconditioners for hp-FEM and nonlocal methods. On the ML side, I’m interested in neural operators, physics foundation models, deep learning theory, and mechanistic interpretability.
Selected publications
- S. Jiang, A. Voronin, E. Cyr, and B. Southworth, On the Convergence Behavior of Preconditioned Gradient Descent Toward the Rich Learning Regime, ICLR, 2026.
- M. Ainsworth and S. Jiang, Uniform Substructuring Preconditioners for High Order FEM on Triangles and the Influence of Nodal Basis Functions, SIAM J. Numer. Anal. 62(4), 2024.
- S. Jiang and C. Glusa, A Splice Method for Local-to-Nonlocal Coupling of Weak Forms, Comput. Methods Appl. Mech. Engrg., 2024.
- S. Jiang, J. A. Actor, S. A. Roberts, and N. Trask, A Structure-Preserving Domain Decomposition Method for Data-Driven Modeling, arXiv preprint, 2024.
- M. Ainsworth and S. Jiang, A Systematic Approach to Constructing Preconditioners for the hp-Version Mass Matrix on Unstructured and Hybrid Finite Element Meshes, SIAM J. Sci. Comput. 44(2), 2022.
- M. Ainsworth and S. Jiang, Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra, SIAM J. Sci. Comput. 43(1), 2021.
- M. Ainsworth, S. Jiang, and M. A. Sanchéz, An O(p³) hp-Version FEM in Two Dimensions: Preconditioning and Post-Processing, Comput. Methods Appl. Mech. Engrg. 350, 2019.
- M. Ainsworth and S. Jiang, Preconditioning the Mass Matrix for High Order Finite Element Approximation on Triangles, SIAM J. Numer. Anal. 57(1), 2019.
Elsewhere
I used to play clarinet at a decently high level, but now am fumbling around in HSCO. I started taking photographs. I also post a lot on Google Maps because I’m a bougie foodie sometimes.
Take 4 at a stable blog; you might be able to find my earlier attempts scattered around the web. All content posted here represents my own personal opinions and should not reflect on anyone else.
To contact me: marshall “period” jiang at google’s email dot com.