# Prof. Justin Sirignano

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

- "Mean Field Analysis of Neural Networks: A Law of Large Numbers" (with K. Spiliopoulos). SIAM Journal on Applied Mathematics, 2020.
- "Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem" (with K. Spiliopoulos). Stochastic Systems, 2020.
- "Inference for large financial systems" (with G. Schwenkler and K. Giesecke). Mathematical Finance, 2020.
- "Mean Field Analysis of Deep Neural Networks" (with K. Spiliopoulos). Mathematics of Operations Research, 2021. arXiv: 1903.04440, 2020.
- "Universal features of price formation in financial markets: perspectives from Deep Learning" (with Rama Cont). Quantitative Finance, 2019.
- "Mean Field Analysis of Neural Networks: A Central Limit Theorem" (with K. Spiliopoulos). Stochastic Processes and their Applications, 2019.
- "Global Convergence of the ODE Limit for Online Actor-Critic Algorithms in Reinforcement Learning" (with Z. Wang). Minor Revision at Stochastic Systems. arXiv:2108.08655, 2021.
- "Deep Learning Closure of the Navier-Stokes Equations for Transitional Flows" (with J. F. MacArt and M. Panesi). Proceedings of AIAA Scitech (2022) and accepted for publication at the AIAA Journal (2023).
- "Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations" (with Ziheng Wang). arXiv: 2202.06637. Mathematical Finance, 2023.
- "Online Adjoint Methods for the Optimization of PDEs" (with K. Spiliopoulos). Applied Mathematics and Optimization, In Press, 2022.
- "DPM: A deep learning PDE augmentation method with application to large-eddy simulation" (with J. F. MacArt and J. B. Freund). Journal of Computational Physics, 2020.
- "Embedded training of neural-network subgrid-scale turbulence models" (with J. F. MacArt and J. B. Freund). Physical Review Fluids, 2021.
- "PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence" (with J. F. MacArt and K. Spiliopoulos). arXiv:2105.08633, Journal of Computational Physics, accepted for publication, 2023.
- "Neural Q-learning for solving Elliptic PDEs" (with S. Cohen and D. Jiang). https://arxiv.org/abs/2203.17128, Journal of Machine Learning Research, 2023.
- "A Forward Propagation Algorithm for Online Optimization of Nonlinear Stochastic Differential Equations" (with Z. Wang). https://arxiv.org/abs/2207.04496, 2022.
- "Deep Learning Closure Models for Large-Eddy Simulation of Flows around Bluff Bodies" (with J. MacArt). https://arxiv.org/abs/2208.03498, Accepted at the Journal of Fluid Mechanics, 2023.
- "Kernel Limit of Recurrent Neural Networks Trained on Ergodic Data Sequences" (with S. Lam and K Spiliopoulos). arXiv:2308.14555, 2023.
- "Global Convergence of Deep Galerkin and PINNs Methods for Solving PDEs" (with D. Jiang and S. Cohen). arXiv:2305.06000, 2023.

Courses: Deep Learning, Machine Learning, Partial Differential Equations, Stochastic Models, Financial Mathematics

Course director of the Oxford Masters program in Mathematical & Computational Finance

Career Placement of PhD Students: Lei Fan (J.P. Morgan Systematic Trading), Xiaobo Dong (J.P. Morgan Machine Learning), Deqing Jiang (Bank of America Fixed Income)

Ranked Excellent in Teaching for a graduate course on deep learning with two hundred students.

See my CV for a complete list of publications and presentations.

Research areas: Stochastic Analysis, Machine Learning, Mathematical Finance, Scientific Machine Learning

Grants:

Office of Naval Research (ONR): $1 million grant in collaboration with Jonathan MacArt (Notre Dame) and Marco Panesi (UIUC)

NSF-EPSRC: $750,000 grant in collaboration with Jonathan MacArt (Notre Dame)

DMS-EPSRC: $847,000 grant in collaboration with Konstantinos Spiliopoulos (Boston University)

Industrial and Government funding: 1 postdoctoral researcher (2 years), 2 PhD students (4 years each)

Co-I for EPSRC Hub for Mathematical and Computational Foundations of AI (2024-)

Co-PI on $16.5 million DoE Center for Exascale-enabled Scramjet Design at UIUC (2020-2021).

Computational grants:

1.5 million GPU hours from DoE's SummitPlus program (2024)

160,000 GPU hours from EPSRC (2024)

3 million GPU hours from the DoE's Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program (2023)

44 million core hours on Blue Waters supercomputer (2016-2020)

120,000 GPU hours on the Summit supercomputer (2020-2021)

Editorial positions: Associate Editor for Mathematical Finance, Managing Editor for Quantitative Finance, Associate Editor for Special Issue of Management Science on Data Science.

Seminars and invited presentations in Years 2020-2022: Imperial College Dept. of Mathematics, Oxford Engineering, Google DeepMind, Two Sigma Investments, Isaac Newton Institute at Univ. of Cambridge, NSF Workshop on Machine Learning in Dallas, Brown University Dept. of Applied Mathematics, London Business School, UCLA Dept. of Mathematics, SIAM Conf. on Financial Math, and SIAM Conf. on Dynamical Systems.

Faculty Member in the Center for Hypersonics and Entry Systems Studies (CHESS)

Faculty Member in the Center for Mathematics of Random Systems

E-Mail: @email

Justin is a Professor of Mathematics at the University of Oxford whose research focuses on Applied Mathematics, Machine Learning, and High-Performance Computing. His research has developed new mathematical theory and numerical methods in finance, deep learning, and scientific machine learning.

He has contributed to the mean-field analysis of deep learning models, including multi-layer neural networks, reinforcement learning, and recurrent neural networks. Another area of interest has been the development and rigorous mathematical analysis of machine learning methods for stochastic differential equations (SDEs) and partial differential equations (PDEs).

In parallel, Justin's research group and collaborators have worked on several application areas. In mathematical finance, they have developed deep learning models for large financial datasets such as: high-frequency data from limit order books, loans, and options. He is also developing deep learning methods for constructing partial differential equation (PDE) models from data, which has a variety of applications in science, engineering, and finance. This includes recent work in the area of "scientific machine learning" on developing deep learning-based PDE models as reduced-order simulations for computationally-challenging physics (e.g., turbulence and hypersonics).

Justin received his PhD from Stanford University and holds a Bachelors degree from Princeton University. He was a Chapman Fellow at the Department of Mathematics at Imperial College. He was awarded the 2014 SIAM Financial Mathematics and Engineering Conference Paper Prize.