Vanderbilt University is inviting applications from prospective doctoral students interested in computational fluid dynamics, scientific machine learning and advanced numerical methods to join a research group in the Department of Mechanical Engineering. The research group is recruiting two fully funded PhD students with an anticipated start date of Spring 2027. The positions are designed for motivated researchers interested in developing advanced computational methods and machine learning approaches for fluid dynamics and engineering applications. The opportunity is open to both domestic and international applicants, including candidates from mechanical engineering, aerospace engineering, applied mathematics, computer science, computational science and related disciplines. Fully Funded Vanderbilt PhD Positions – Key Details University: Vanderbilt University Department: Mechanical Engineering Positions: 2 PhD students Expected start: Spring 2027 Funding: Fully funded Stipend: Starting at $40,000 per year Tuition: Fully covered Health insurance: Individual health insurance covered Relocation: Relocation allowance provided Student fees: Student activity and recreation fees covered Application track: CFD or Scientific Machine Learning Initial contact: ahmad.peyvan@vanderbilt.edu Formal application encouragement: Candidates with strong research fit will be encouraged to apply by October 15, 2026 Research Track 1: Computational Fluid Dynamics with Scientific Machine Learning The first research track focuses on combining advanced computational fluid dynamics techniques with scientific machine learning. Research areas may include high-order numerical methods, DGSEM, compressible and high-speed flows, adaptive and high-performance computing, machine-learning-assisted solvers and reduced-order modelling. Students working on this track will have the opportunity to explore computational approaches for solving complex fluid dynamics problems while investigating how machine learning can improve the efficiency and capabilities of traditional numerical methods. Potential research directions include developing more efficient computational solvers, improving numerical simulations of high-speed flows and integrating machine learning techniques into high-performance computing workflows. The track is particularly relevant to applicants interested in computational mechanics, numerical analysis, fluid dynamics and the intersection between traditional simulation methods and artificial intelligence. Research Track 2: Scientific Machine Learning for Fluid Dynamics The second research track focuses more directly on the application and development of scientific machine learning methods for fluid dynamics. Research areas include neural operators, physics-informed neural networks, geometry-dependent surrogate modelling, reduced-order modelling, scientific foundation models and integration of learned models with numerical solvers. Students may investigate how modern machine learning architectures can learn physical systems and accelerate computational simulations while maintaining important physical constraints. The research can involve developing surrogate models for complex engineering systems, designing neural-network-based approaches for fluid simulations and integrating learned models with established numerical solvers. This track could be particularly attractive to applicants with interests in artificial intelligence, computational science, machine learning, numerical methods and engineering simulation. Applicants Do Not Need Expertise in Both Fields An important feature of the opportunity is that prospective students do not need to already be experts in both computational fluid dynamics and machine learning. Applicants with a strong foundation in one relevant area and an interest in developing expertise across the intersection of CFD and scientific machine learning are encouraged to apply. The research group is particularly interested in candidates who demonstrate strong research potential, technical curiosity and a clear interest in computational approaches to fluid dynamics. Eligible Academic Backgrounds Applications are encouraged from candidates with academic backgrounds in: Mechanical Engineering Aerospace Engineering Applied Mathematics Computer Science Computational Science Related engineering and quantitative disciplines Both domestic and international students are encouraged to express their interest. Applicants should demonstrate preparation relevant to their selected research track. Experience with numerical simulation, programming, computational mathematics, fluid dynamics or machine learning can strengthen an application, depending on the proposed research direction. Fully Funded PhD Package The positions currently include a comprehensive funding package designed to support doctoral students throughout their studies. The package includes a stipend starting at $40,000 per year, providing financial support for living expenses. Selected students will also receive full tuition support, meaning tuition costs associated with the doctoral programme will be covered. In addition, the funding package includes paid individual health insurance, a relocation allowance and coverage of student activity and recreation fees. The combination of tuition coverage, stipend and additional benefits makes the opportunity particularly relevant for students seeking fully funded doctoral research opportunities in the United States. How Interested Students Can Apply Prospective students are encouraged to review the research announcement carefully before contacting the research group. Interested candidates should email the requested application materials to: ahmad.peyvan@vanderbilt.edu Applicants should use one of the following email subject formats: Prospective PhD Student – CFD Track – [Your Name] or Prospective PhD Student – SciML Track – [Your Name] Candidates should clearly indicate which research track they are interested in and provide the materials requested in the announcement. The initial contact is intended to help the research group assess research fit before candidates proceed with the formal university application process. Formal Application Deadline Candidates who demonstrate a strong research fit will be encouraged to proceed with a formal PhD application. The target date for submitting the formal application is October 15, 2026, while the anticipated programme start is Spring 2027. Students interested in pursuing advanced research at the intersection of computational fluid dynamics, numerical methods and artificial intelligence are encouraged to begin preparing their materials early. Why Consider This Opportunity? These PhD positions provide an opportunity to conduct research at the intersection of fluid dynamics, high-performance computing and artificial intelligence while working within a mechanical engineering research environment at Vanderbilt University. The two complementary tracks allow students to pursue either computational fluid dynamics enhanced by machine learning or machine learning approaches specifically designed for fluid dynamics. For students interested in the future of engineering simulation and scientific computing, the research could provide valuable experience in areas such as neural operators, physics-informed learning, high-order numerical methods, reduced-order modelling and machine-learning-assisted computational solvers. 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