Mathematical models and numerical methods for problems without an off-the-shelf solver.
Model formulation, discretisation, convergence analysis, physics-informed learning and foundation models for simulation, built to run at industrial size.
- 01Equations first
- A new material, a coupling not done before, a scale where the usual assumptions fail. For each of these we write the governing equations for your system and say what they assume.
- 02Proven to converge
- A discretisation chosen for the problem, with the analysis and the verification study that let an engineer trust the output as well as reproduce it.
- 03Learning that keeps the physics
- Surrogates, neural operators and foundation models for simulation that respect the conservation laws, so the fast result obeys the same conservation laws.
01Capabilities
What we do
- Mathematical modelling
The governing equations, written for your system.
- Continuum mechanics, thermodynamics and transport formulations
- Multiscale models bridging molecular, meso and continuum descriptions
- Inverse problems for parameter identification and design
- Poromechanics, with flow and deformation coupled in porous media
- Numerical methods
Discretisations designed for the problem, with the analysis to back them.
- Finite element, finite volume and spectral methods with convergence analysis
- Stabilisation for advection-dominated and saddle-point problems
- Multigrid and Krylov solvers for large sparse systems
- Adaptive refinement driven by a posteriori error estimates
- PDE-constrained optimisation
Design and control where the constraint is a differential equation.
- Adjoint methods for gradients in high-dimensional design spaces
- Shape and topology optimisation under PDE constraints
- Optimal control of distributed systems
- Applications in aerodynamics, structures, RF and biomedical flow
- Physics-informed learning
Machine learning that keeps the conservation laws.
- Neural ODEs and multilevel training methods
- Conservation-respecting architectures and losses
- Surrogates for simulation acceleration
- Foundation models for simulation
Trained on simulation data, fine-tuned on your cases, checked against the full solver.
- Neural operators trained across geometries and operating conditions
- Physics-verified surrogates that reduce set-up and solve time
- Small models trained for one domain
- Every prediction checkable against a full solve
- 01Model formulation with stated assumptions
- 02Convergence and verification study
- 03Reference implementation with tests
- 04Technical report, publishable where you allow it
- 05Handover to your engineering or research team
02Common problems
Problems we solve.
01The current tools cannot handle the problem.
The problem is formulated and the existing methods are surveyed. The findings state which method suits it and what building it would take.
02The method exists in a paper and nowhere else.
We take it from the paper to code with tests, documentation and a convergence study, built to a standard an engineer can use.
03The simulation is right but takes a week per case.
A physics-informed surrogate or a simulation foundation model, verified against the full solver, for the design loop.
04Nobody can say whether the numbers converge.
A posteriori error estimates, adaptive refinement and a verification report with the error quantified.
Tell us your pain points.