Often the bottleneck is writing the solver, not running it

GPUs keep making large simulations cheaper to run. What still takes weeks is everything around the run: choosing a numerical scheme, implementing it by hand, hunting the sign error that gives a plausible but wrong answer, and validating the result. Many production solvers are also locked inside legacy CPU code, where a GPU port is a multi-million-euro refactor.

AI agents can help, but relying on general-purpose array frameworks means they juggle indexing, staggering, boundaries and memory layout alongside the physics. The resulting code is costly to generate, hard to maintain, and fails the human review that end users require.

What Sofia is

Sofia pairs a physics language with an agent that knows how to use it.

• The Sofia DSL. Simulations are written at the level of the equations, on top of SymPy. Stencils, boundary conditions, staggered grids and time-stepping are lowered automatically, and CAD geometries are first-class. An incompressible Navier–Stokes solver is twelve lines of Sofia versus several hundred lines of hand-written kernels, and changing the physics is a one-line edit.
• The Sofia agent. It picks the physics and numerical schemes, builds and runs the solver, and checks things like conservation, boundary behaviour and grid convergence. It returns a short, reviewable Sofia program with a validation report, not a black box.
• Built on NVIDIA Warp and JAX. Sofia emits per-cell updates as Warp kernels and orchestrates them with JAX, so the emitted code is GPU-native and auto-differentiation through a full solve works out of the box. Warp's mesh queries let Sofia handle complex geometry without leaving the GPU. The same script also runs on CPU.

Proof point: the river Waal

With Deltares and the Dutch Ministry for Infrastructure and Water Management, we asked Sofia's agent to compute steady-state water depth and velocity along 85 km of the Waal, the Rhine's main distributary in the Netherlands, on a 2.3-million-cell bathymetry grid at 25 m resolution. We fixed the bed and boundary conditions, and left the choice of equations and numerical method to the agent.

• Under 30 minutes and €1.87 in tokens to a validated solver, after the agent tested several schemes, two flooding-and-drying treatments and the need for eddy viscosity.
• Under 13 cm deviation from Deltares' reference at all 96 observation points, beating our own hand-built Sofia solver (within 40 cm).
• Still accurate at 50 m resolution (average deviation 6.5 cm → 7.1 cm), at a quarter of the memory footprint. Our hand-built solver wasn’t able to run at 50 m resolution.

Our first hand-built solver for this problem took months to write and validate, and over a year to match Deltares' software. A precursor to Sofia cut that to weeks; the agent now does it in minutes.

With Fermioniq's technology, I expect that the development of the solver and associated applications can be reduced from the order of days to the order of a few hours compared to our current approach. — Dr. Hans van Putten, Director of Digital Strategy, Deltares

Read our blog post: From a Prompt to a Validated Solver: Fermioniq's Sofia Brings Agent-Built Physics to NVIDIA GPUs

More examples

What Sofia has already built:

• River flow along the Waal, checked against Deltares’ reference
• Flow around the Ahmed body, with drag computed within 3% of the reference
• Urban wind flow through Amsterdam Science Park on an NVIDIA GH200

See here for more details: https://fermioniq.github.io/sofia-showcase-page/