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Computational Mathematician - Machine Learning startup

Use your research-level numerical analysis and programming skills to help us develop our ML-accelerated computational fluid dynamics simulation software.


Compensation: £50,000 salary + equity options.

Contract: Permanent, full-time.

Work location: In-person, Cambridge (~10-minute walk from the train station).

Start date: Ideally by April 2024.

Role Summary

We are looking for a computational mathematician with strong experience in numerical analysis and programming to join our early-stage fluid simulation startup. Collaborating with our team of mathematicians and machine learning engineers, you will be driving forward the development of our flagship ML accelerated CFD product. Help us in extending cutting-edge machine learning and numerical analysis techniques to bring order-of-magnitude efficiency gains to engineering users.


As an early-stage startup, we expect your responsibilities will evolve based on the company’s development and your career ambitions. However, in the short term, your primary responsibility is to collaborate with our team to drive forward the development of our 2D ML accelerated computational fluid dynamics solver. This will include but is not limited to:

  • Optimise how we solve the systems of equations core to CFD (solver selection, preconditioners, tolerances).
  • Identify meshing techniques to integrate with cutting-edge machine-learning techniques.
  • Implement additional features key to industrial-grade CFD software, including support for various types of mesh and turbulence models (e.g. RANs, LES).
  • Learning the software engineering skills required to write industrial-grade software.
  • Participating in code review with the team (i.e. we review your code, but you also review ours).
  • Stay up to date with recent research in numerical analysis and ML by reading papers.

About you

You should have:

  • Research level understanding of numerical analysis techniques for solving PDEs, such as:
    • Finite volume methods.
    • Iterative solvers e.g. conjugate gradients.
    • Mesh generation algorithms, for grids such as unstructured, non-uniform, quad/octree.
    • Preconditioners.
    • Multigrid solvers.
  • Numerical/array programming experience.
  • Interest in learning ML methods.

It would be nice for you to have:

  • Experience in Python and JAX.
  • Exposure to machine learning methods for solving PDEs (e.g. Neural Operators, PINNs, PDE discovery).
  • Knowledge of fluid dynamics.
  • Hands-on experience designing and debugging novel deep-learning architectures.
  • Commercial software engineering experience.

What you will learn

We will give you opportunities to learn new skills (and for us to learn from you) through fostering a peer learning environment, whether that be through code review, at the whiteboard or joining customer calls. Examples of what you can learn:

  • Industry-standard software engineering tools and practices (e.g. version control, unit testing, software design).
  • Cloud computing and backend web development.
  • The fundamentals of machine learning applied to numerical computing problems.
  • The non-technical skills required to help run an early-stage startup (e.g. presentations, talking to customers, recruiting).


  • Salary of £50,000 and equity options.
  • 25 days of annual leave plus bank holidays.
  • Top-of-the-range hardware, peripherals and ergonomic office equipment.
  • Flexible working arrangements for those with dependents.
  • Fancy espresso machine.
  • Experience the excitement of an early-stage startup with a huge amount of freedom in your work and the ability to guide the development of our core product.
  • Use your technical expertise to create next-generation simulation tools to help engineers overcome critical problems in aerospace, Formula 1, energy and biomanufacturing.
  • Opportunity to transform this role into a leadership position as the company grows.

About Vanellus

Computational fluid dynamics (CFD) simulations are increasingly in demand by engineers, and traditional tools have struggled to keep pace with the growing computational requirements. At Vanellus, we are solving this problem by developing radically more efficient CFD using machine learning.

Founded in 2022, the team comprises the company founders, Laurence Cullen (6 years in startups as an ML engineer) and Dr. Michael Negus (Oxford applied maths PhD in fluid dynamics and DNS) in addition to mathematical engineer Dr. Aditi Roy (previously a postdoc at the Oxford Computer Science department researching electrical cardiac modelling on GPUs).

So far, we have developed and validated our core differentiable 2D solver against a range of benchmarking problems and are working on expanding the range of problems we can simulate. Simultaneously we are implementing and improving machine learning approaches to radically improve the efficiency of our core solver. You can read more about our progress in our blog.

Apply now