Vanderbilt University is seeking two students for a fully funded PhD in Computational Fluid Dynamics at Prof. Ahmad Peyvan’s laboratory in the Department of Mechanical Engineering starting in spring 2027.
Such positions provide an excellent chance for interested candidates to carry out research in the field that involves the intersection between CFD, high-performance scientific computing, applied mathematics, and SciML. All domestic and international applicants are encouraged to apply for the positions.
Research Opportunities
The team creates sophisticated mathematical and data-centric techniques to create accurate models of complex fluid dynamics systems. The students will engage in an interdisciplinary project involving physical modeling, numerical simulation, machine learning, and state-of-the-art scientific software engineering.
There are two complementary Ph.D. research paths.
Track 1: Computational Fluid Dynamics with Scientific Machine Learning
This track is designed for students interested in high-fidelity numerical simulation, computational mechanics, and machine-learning-enhanced scientific computing.
Potential research topics include:
- High-order numerical techniques such as the discontinuous Galerkin spectral element method (DGSEM)
- Simulating compressible and fast flows with shock waves and complicated physical phenomena
- Adaptive numerical approaches and high-performance computing
- Numerical solvers augmented with machine learning
- Reduced-order modeling and simulation data analytics
Applications from candidates with experience in mechanical engineering, aerospace engineering, applied math, computational sciences, or a similar discipline are welcome. Prior knowledge of fluid mechanics, numerical methods, partial differential equations, or computer languages like Julia, C++, or FORTRAN is highly valued.
Track 2: Scientific Machine Learning for Fluid Dynamics
In this module, we will explore how to employ modern machine learning techniques to solve problems related to fluid dynamics and partial differential equations.
Topics for investigation may include:
- Neural Operators and geometry-dependent surrogate models for PDE-driven problems
- Physics-aware and structure-aware machine learning techniques
- Reduced order modeling and Scientific Foundation Models
- Interpretability, generalizability, and robustness through high-fidelity simulation data
- Combination of learned models with traditional numerical solvers
We especially encourage those with prior exposure or an interest in machine learning, data science, PDE numerics, scientific computing, or computational engineering to apply. Knowledge of Python, PyTorch, TensorFlow, JAX, or similar packages is desirable.
PhD in Computational Fluid Dynamics Funding Package
The selected Ph.D. students will receive a comprehensive funding package through the Vanderbilt School of Engineering. Current support includes:
- Annual stipend beginning at $40,000
- Tuition remission
- Health insurance for individuals paid by the institution
- Moving expense allowance
- Student activities/athletic fee subsidy
- Additional fellowships varying between $1,000 and $10,000 annually, dependent upon availability and success in the program
Funding is contingent on satisfactory academic progress and successful performance of assigned research or teaching responsibilities.
PhD in Computational Fluid Dynamics Training and Research Environment
Training will be given according to students’ research background, interest, and changing academic goals. Neither a CFD nor a machine learning background is necessary. Students can choose one path to enter and gain complementary skills while doing the Ph.D.
The lab offers possibilities to
- Have access to high-performance computing systems
- Collaborate with scientists working in areas of computational mechanics, applied mathematics, and machine learning
- Work with industrial collaborators on applied problems
- Attend research seminars, mentoring sessions, and software development collaborations
- Deliver talks and write papers on fluid mechanics, scientific computing, and machine learning
- Build robust, reproducible and high-performance research software
PhD in Computational Fluid Dynamics Qualifications
Strong applicants will demonstrate several of the following:
- Strong academic foundation in engineering, applied mathematics, computer science, or any related field
- Course/project/research work in computational fluid dynamics, numerical methods, scientific computing, or machine learning
- Programming skills using languages such as Julia, C++, C, Fortran, Python, or equivalent
- Research aptitude evident in the form of a thesis, publication, or any major project
- Interdisciplinary research interest between physical models and machine learning
The candidates do not need to be an expert in both CFD and machine learning. What is important for the group is that the candidate should have knowledge in at least one of the fields.
How to Apply
Interested students should email Prof. Ahmad Peyvan at [email protected] before submitting an official Vanderbilt application.
Please include the following materials:
- Curriculum vitae
- Academic transcripts not on official letterhead
- A short description of about one page in length of your research interests, track preference, experience, and contribution to teamwork
- Optionally, a sample publication, thesis, project, or software code repository
Use the following email subject line:
Prospective PhD Student – [CFD Track or SciML Track] – [Your Name]
After a first email conversation and virtual meeting, candidates whose research background is compatible may be invited to submit an application to the Ph.D. Program in Mechanical Engineering at Vanderbilt University. The application deadline is October 15, 2026.
Share This Opportunity
This is a great chance for those students who aim to contribute to the advancement of the field of computational fluid dynamics, scientific machine learning, high-performance computing, and physics-based modeling.
Potential candidates are recommended to go through the full announcement and communicate with Prof. Ahmad Peyvan for a research match. Please pass this information on to those qualified individuals you know.
Frequently Asked Questions
Are these Ph.D. positions fully funded?
Yes. The current funding package consists of a stipend amounting to $40,000 per annum, tuition coverage, health insurance, relocation expenses, and payment for students’ activities/recreation fees. Renewal of the funding is contingent upon satisfactory academic standing and assigned research/teaching duties.
How many Ph.D. positions are available?
There are two fully funded PhD positions in Prof. Ahmad Peyvan’s group within the Mechanical Engineering Department at Vanderbilt University.
When will the Ph.D. program begin?
The expected starting date is spring 2027.
What research tracks are available?
Applicants can express interest in one of two tracks:
- Computational Fluid Dynamics Using Scientific Machine Learning based on high-order numerical methods, high-speed flows, adaptive computing, ML-assisted solvers, and reduced-order modeling.
- Scientific machine learning for fluid dynamics using neural operators, physics-informed machine learning, surrogate modeling, scientific foundation models, and machine learning models coupled with numerical solvers.
Do I need expertise in both CFD and machine learning?
Not. The applicants are not required to have experience in both domains. Applicants who have expertise or interest in either of the fields, like CFD or machine learning, are welcome to apply, and the training would be customized according to the interests of the student.
Which academic backgrounds are suitable?
Students majoring in mechanical engineering, aerospace engineering, applied mathematics, computer science, computational science, data science, and related fields are strongly encouraged to apply.
What skills are preferred for the CFD track?
Good preparation would include some familiarity with fluid mechanics, computational fluid dynamics, numerical methods, partial differential equations, scientific computing, and/or high-performance computing. Familiarity with programming in Julia, C++, C, or Fortran is also a plus.
What skills are preferred for the SciML track?
The relevant background for preparation would include machine learning, numerical partial differential equations, data science, scientific computing, or computational engineering. Relevant experience with programming languages like Python and tools like PyTorch, TensorFlow, and JAX is beneficial.
Can international students apply?
Yes. Applications from both domestic and international candidates are accepted. Candidates are recommended to visit Vanderbilt University’s website to learn more about the graduate application process.
What materials should I email to Prof. Peyvan?
Interested candidates should send:
- Curriculum Vitae
- Unofficial Transcripts
- One page detailing areas of interest, preference of track, previous experience, and personal role in teamwork
- Optionally, one paper, thesis, project, or source code repository
What email subject line should I use for the PhD in Computational Fluid Dynamics position?
Use the following format:
Prospective PhD Student – [CFD Track or SciML Track] – [Your Name]
For example:
Prospective PhD Student – SciML Track – Jane Doe
Should I contact the professor before submitting an application for a PhD in Computational Fluid Dynamics?
Yes. Interested applicants should first email Prof. Ahmad Peyvan at [email protected]. After an initial email exchange and online meeting, candidates with a strong research fit may be encouraged to submit a formal application to Vanderbilt’s Mechanical Engineering Ph.D. program.
What is the formal application deadline for PhD in Computational Fluid Dynamics?
Candidates who are encouraged to apply formally should aim to submit their Vanderbilt Ph.D. application by October 15, 2026.
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