Research Intern 2027 - PDEs

Job Description

Job Title: Research Intern 2027 (3 months) - Algorithms and Applications for PDEs. Location: Dublin, Ireland

Job type: Internship, hybrid, fixed-term for 3 months

Responsibilities:

• Contribute to research on quantum-centric supercomputing, combining quantum computing, artificial intelligence, and conventional numerical methods to improve the performance of forward and inverse partial differential equation (PDE) problems.

• Develop and evaluate quantum solvers, physics-informed AI models, neural operators, and data assimilation methods;

• Implement quantum algorithms, train AI models, validate performance across different computational approaches, and develop cross-platform workflows, depending on your background and research opportunities.

• Investigate challenges in quantum PDE applications, including state preparation, measurement and readout, scalability, and computational efficiency.

• Develop and validate workflows that combine scientific computing, machine learning, and quantum algorithms for real-world applications.

Required:

• Master's degree.

• Working understanding of partial differential equations (PDEs), from either a theoretical or application-oriented perspective.

• Knowledge of statistics.

• Proven experience prototyping in Python, particularly with NumPy.
• Research experience in at least one of the following areas:
  • Applied mathematics, particularly differential equations, operator-theoretic methods, or numerical linear algebra for large-scale systems.
  • AI models for PDEs.
  • Quantum computing.

Preferred qualifications:

• Experience with neural operators and AI models for inverse problems.

• Experience with physics-informed learning for scientific AI models.

• Experience with data assimilation methods, including variational data assimilation (3D-Var, 4D-Var), Kalman filtering, or score-based AI data assimilation.

• Experience with quantum algorithms and methods, including Hamiltonian simulation, linear combinations of unitaries (LCU), quantum signal processing (QSP), singular value transformation (SVT), qubitization, block-encodings, amplitude amplification and estimation, phase estimation, or quantum linear systems methods;

• Knowledge of discretization methods, including finite element methods (FEM), finite difference methods (FDM), and spectral methods.

• Experience with PDE solvers such as conjugate gradient (CG), GMRES, and multigrid methods, along with conditioning and preconditioning analysis.

• Background in model reduction techniques, including proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), balanced truncation, or Koopman and Carleman embeddings.

• Strong software engineering skills.

• A record of research publications.

Benefits and work environment:

• Opportunity to work with a global research team developing quantum-centric supercomputing technologies.

• Exposure to research combining high-performance computing, AI, quantum computing, and hybrid cloud technologies.

• Opportunities for learning, professional development, experimentation, and collaboration.

• Supportive environment that encourages curiosity, innovation, feedback, and career growth.

Additional information:

• The position is for a fixed term of three months.

• The work arrangement is hybrid.

• No travel is required.

• The role is not commission-based and does not include sales incentives.

• Applicants can contact the recruiter after applying for further details about location requirements;

• IBM is an equal opportunity employer and considers qualified applicants without discrimination based on legally protected characteristics.

• IBM complies with applicable laws concerning citizenship and immigration status.