Research Focus
The central theme of my research is to use applied analysis, numerical methods, and/or machine learning to better understand physical systems mostly within Hamiltonian, quantum, or nonlinear wave settings. Most of my earlier work, which I still very much enjoy to do today, involves optimal control theory and nonlinear waves.
New and Active Projects (please come to my talks if not published yet)
- Reduced Order Modeling via spectral methods
- Neural methods for long-time integration of PDEs
- Applied analysis of nonlinear waves, lately working on the Manakov system and the Salerno lattice
- Learning structure (integrability, integral transforms, conservation laws, normal forms, etc.) from data
- Data-driven methods in open quantum systems
2026 summarized
- I'll be giving a talk about spectral ROMs at the SIAM Conference on Mathematics of Data Science
- I'm organizing a session (with Rodrigo Platte @ ASU) about quantum computation and will be giving a talk about learning Lax pairs at the AMS Southwest Sectional Meeting 2026
- I'm organizing a session (with Jose Morales @ UTSA) on quantum machine learning and giving a talk about rogue waves at the SIAM TX-LA sectional meeting
- I'll be giving a talk about the dispersionless Manakov system at the SIAM NY-NJ-PA sectional meeting
- I gave a talk about discrete rogue waves at a conference honoring Michael Herrmann in Leiden.
- I gave a talk about discrete rogue waves at the AIMS conference in Athens, Greece.
- I particpated in an ICERM workshop on nonlinear waves being held from April 27 - May 1, 2026.
- I received a SIAM Science Policy Fellowship
- I am now an affiliate of the Simon A. Levin Mathematical, Computational, and Modeling Sciences Center
- Wei Zhu (@ Georgia Tech) and I organized a minisymposium at SIAM NWCS '26 on structure preserving learning for nonlinear waves.
- We had a gathering on Jan 30th @ ASU to discuss the future of postdoc development programs.
- I gave a talk about spectral model reduction at Dynamics Days on January 9th.
Contact
For questions about research, collaboration, or student opportunities, please email me: jimmie.adriazola [at] asu [dot] edu