Job Description

We are seeking outstanding candidates with a strong track record of high performance in academic or industrial settings. You will play a central role in developing and implementing advanced mathematical models that power the ToffeeX engineering design platform.


This is an opportunity to work at the intersection of mathematics, engineering, and technology within a rapidly growing company. You'll join a multidisciplinary team solving challenging real-world problems, with a focus on physics simulation, optimisation, and computational geometry.

Key Responsibilities:

Design and implement novel algorithms to tackle complex multi-physics simulation and PDE-constrained optimisation problems. Collaborate closely with engineers and developers to integrate new capabilities into our cloud-based design software, directly impacting customer outcomes. Contribute across the full software development lifecycle, from conceptual design to deployment and support. Work with customer success engineers to understand user needs and tailor solutions accordingly. Go beyond existing literature to develop creative, effective solutions to unique real-world engineering problems.

Essential Skills & Experience

Ph.D. in Applied Mathematics, Physics, Engineering, or a closely related field. Research-level experience in one or more of the following areas: + Physics-based simulation using FVM or FEM, including fluid, thermal, structural, or coupled multi-physics models.
+ PDE-constrained optimisation, such as optimal control, shape, or topology optimisation.
+ Mathematical optimisation, including robust, non-convex, or high-dimensional optimisation problems.
+ AI/ML techniques for physics simulation or optimisation problems.
+ Mathematical modelling and model reduction.
+ Computational geometry and meshing, including shape parametrisation, CAD integration, and mesh generation or adaptation.
Extensive hands-on experience in developing and implementing numerical algorithms in one or more of the above areas. Comfortable working in a fast-paced, collaborative environment.

Desirable Skills & Experience:

Experience taking technical ownership of projects or leading teams. Software development experience in C++ and Python. Experience with CFD frameworks such as OpenFOAM, SU2, or similar simulation tools.

Company Benefits

Flexibility and support for continuous learning and professional growth. 25 days holiday per annum (plus UK bank holidays). Private Healthcare with Vitality Health.
Pension Scheme with NEST. Cycle to Work scheme. Perks at Work - Access to 30,000+ national & local employee discounts. Work From Home Fridays. Frequent Team Socials. Visa Sponsorship Options.

Available once probationary period is complete

About us:

At ToffeeX, we are revolutionizing engineering design with our innovative software. This cutting-edge tool automates the creation of mechanical components for the engineering industry, leveraging advanced artificial intelligence, numerical simulation, and sophisticated mathematical optimization techniques. By bringing these innovations to the cloud, we empower design engineers to create components that outperform existing solutions.


We are committed to integrating the latest mathematical research into practical industry applications. Our cloud platform, built on a microservice architecture, allows us to continuously deploy advanced algorithms in optimization, computational geometry, and machine learning, keeping us at the forefront of engineering design technology.


Due to our recent growth, we have moved into a new office based in Central London where the team have a great space for collaboration. We have a fantastic culture within the company where each one of our team members is dedicated to helping ToffeeX become the best in the industry. ToffeeX has recently been named in the Startups.co.uk (https://www.linkedin.com/company/14033268/admin/page-posts/published/?share=true) 100 Index 2025!


If you think this role is for you, please submit your application and we look forward to hearing from you!