Two Fully Funded Ph.D. Positions in CFD and SciML-Vanderbilt University

Prof. Ahmad Peyvan’s research group in the Department of Mechanical Engineering at Vanderbilt

University invites applications for fully funded Ph.D. positions in computational fluid dynamics (CFD),

scientific machine learning (SciML), and high-performance scientific computing. The group develops

computational and data-driven methods for reliable modeling of complex fluid-flow systems.

Number of openings: 2

Funding: Funding includes a stipend at the Vanderbilt School of Engineering rate (currently starting at

$40,000 per year), full tuition support, paid individual health insurance, relocation allowance, and covered student activity and recreation fees. Continued support is contingent on satisfactory academic progress and satisfactory performance of assigned research or teaching responsibilities. Eligible, highly qualified applicants may also be considered for competitive supplemental fellowships of $1, 000−$10,000 per year.

Students will receive interdisciplinary training spanning computational mechanics, applied mathematics, and artificial intelligence. Two complementary research tracks are available; applicants may work across both tracks as their interests develop.

Track 1: Computational Fluid Dynamics with Scientific Machine Learning

This track is intended for students whose primary interest is computational fluid dynamics and numerical methods. Potential research areas include:

• High-order numerical methods, including discontinuous Galerkin spectral element methods (DGSEM),
• for nonlinear conservation laws
• Robust simulation of compressible and high-speed flows involving shocks and complex physical processes
• Adaptive and high-performance computational methods
• ML-assisted solvers, simulation analysis, and reduced-order modeling

Applicants with backgrounds in mechanical engineering, aerospace engineering, applied mathematics,

computational science, or related disciplines are encouraged to apply. Experience with fluid mechanics, numerical methods, partial differential equations, or scientific programming in Julia, C++, or Fortran is desirable.

Track 2: Scientific Machine Learning for Fluid Dynamics

This track is intended for students whose primary interest is machine learning for physical and engineering systems. Potential research areas include:

• Neural operators and geometry-dependent surrogate modeling for PDE-governed systems
• Physics-informed and structure-aware machine learning
• Reduced-order modeling and scientific foundation models
• Generalization, robustness, and interpretability using high-fidelity simulation data
• Integration of learned models with numerical solvers

Applicants with backgrounds in computer science, applied mathematics, mechanical engineering, aerospace engineering, data science, or related disciplines are encouraged to apply. Experience with machine learning, numerical PDEs, scientific computing, PyTorch, TensorFlow, JAX, Python, or related tools is desirable.

Training and Collaboration

The balance between CFD and machine learning will be tailored to each student’s background, interests, and research progress. A track preference stated during the application process is not a permanent commitment. Students will have opportunities to:

• Use advanced high-performance computing resources
• Collaborate with researchers in computational mechanics, applied mathematics, and machine learning
• Potentially collaborate with industry partners on relevant real-world problems
• Receive training through research seminars, technical mentoring, and collaborative software development
• Present and publish research in computational science, fluid mechanics, and scientific machine learning
• Develop reliable, reproducible, and high-performance research software

Preferred Qualifications

Strong candidates will demonstrate several of the following:

• Strong academic preparation in engineering, applied mathematics, computer science, or a related
• discipline
• Experience with CFD, numerical methods, machine learning, or scientific computing through course-
• work, research, or projects
• Proficiency in one or more relevant programming languages including Julia, C++, C, or Fortran
• Evidence of research potential through a thesis, publication, substantial project, or research-software
• contribution
• Interest in interdisciplinary research spanning physical modeling and machine learning

Applicants are not expected to have prior expertise in both CFD and machine learning.

Application Process Interested students should email the following materials to ahmad.peyvan@vanderbilt.edu:

1. Curriculum vitae
2. Unofficial transcripts
3. A brief statement (approximately one page) describing research interests, preferred track, relevant
4. experience, and the applicant’s individual contributions to any collaborative work discussed
5. Optionally, one representative publication, thesis, project report, or software repository

In the email subject line, please write:

Prospective PhD Student – [CFD Track or SciML Track] – [Your Name]

Prospective students should contact Prof. Ahmad Peyvan before submitting an official application.

Following an initial email exchange and an online meeting, candidates whose background and research interests appear to be a strong fit will be encouraged to apply formally to the Ph.D. program in Mechanical Engineering at Vanderbilt University by October 15, 2026. An invitation to apply indicates potential research alignment but does not constitute an offer of admission; formal admission decisions are made through the university application process. Selecting a track in the subject line is for initial routing only and does not restrict the student’s eventual research direction.

• Faculty directory: https://engineering.vanderbilt.edu/people/mechanical-engineering/
• Application website: https://apply.vanderbilt.edu/apply/

Domestic and international applicants are welcome. Please consult the official application website for

current degree, testing, English-language, and application-fee requirements.