Postdoctoral Scholar in Applied Mathematics.

Position description

Prof. Harish S. Bhat in Applied Mathematics at UC Merced is seeking applicants for a postdoctoral position in applied / computational mathematics.

The postdoctoral scholar will develop new computational methods that fuse modern machine learning methods with first-principle, time-dependent, nonlinear / nonlocal partial differential equations.

Through this fusion, the postdoctoral scholar will develop methods that learn unknown / missing terms in models of time-dependent physical systems, with the aim of

i) improving the model's accuracy,

ii) reducing the model's dimensionality, and

iii) controlling the system's behavior.

The postdoctoral scholar will work closely with Prof. Bhat and will also be co-mentored by Prof. Christine Isborn (Chemistry, UC Merced).

The postdoctoral scholar will be expected to lead and / or to participate in research projects; this will include pen-and-paper mathematics, development of code, and design / execution of numerical experiments leading to scientific discovery.

The postdoctoral scholar will be expected to coauthor manuscripts for publication in peer-reviewed journals and proceedings, to develop and publish open-source software, to present research findings at conferences / seminars, and to work with graduate and undergraduate student researchers.

Qualifications

Basic qualifications

PhD in Applied Mathematics or related field

Experience developing new computational methods, especially for Hamiltonian / Lagrangian systems (whether classical or quantum) and implementing these methods in code on large-scale computational clusters

Strong verbal and written communication skills

Experience publishing peer-reviewed articles and presenting at conferences / seminars

Preferred qualifications

Preferred qualifications include expertise in at least one of the following areas :

1) machine learning for time-dependent physical systems

2) numerical optimal control

3) constrained nonlinear optimization

4) nonlinear system identification

5) numerical solution of the time-dependent Schrodinger equation and / or related evolution equations that arise in molecular quantum mechanics

Within areas (1) through (4), an emphasis on Hamiltonian / Lagrangian systems, whether classical or quantum, is preferred.

Experience with machine learning frameworks such as JAX, PyTorch, and / or TensorFlow is preferred.