What is a solver?

Physics is written as equations. Most of them cannot be solved with pen and paper. A solver is the computer procedure that finds an approximate answer, one small step at a time. Every simulation, from a walking robot to air flowing over a wing, has a solver at its core.

Solvers inside a robot simulator

In a robot simulator, the solver's job is to find the forces at every joint and every point of contact so that parts stay attached where they should and do not pass through each other. MuJoCo, one of the main engines, turns this into an optimisation problem and offers three different procedures to solve it.^[2]

The solver is a swappable component. The Newton engine ships eight of them, each suited to a different kind of material: one for classic robot arms, one for fast and robust general use, one shared with MuJoCo, others for cloth, and one for sand-like materials.^[1] Choosing a solver means choosing between accuracy, stability and speed.

Solvers for fluids, heat and stress

Air, water, heat and the bending of a metal part are not a few rigid pieces; they are continuous. Their solvers cut the space into millions of tiny cells and compute what flows from each cell to its neighbours. OpenFOAM, the best-known open-source software for fluid flow, is one example; its 2025 release notes describe improvements to exactly this kind of routine.^[4] These calculations take minutes to hours, which is why they live outside robot simulators. More in What is traditional physics-based simulation?

Solvers on graphics cards

A graphics card (GPU) can do thousands of small calculations at the same time, which suits physics well. NVIDIA Warp is a tool that turns Python code into GPU programs, and it is the foundation of both the Newton engine and MuJoCo Warp.^[3] Invisible Force's own physics modules are written in Warp for the same reason.

Letting AI imitate a solver

A surrogate is a neural network trained on many results from a real solver, so that it can predict a similar result in milliseconds instead of hours. NVIDIA PhysicsNeMo, formerly called Modulus, is a toolkit for building them.^[5] A 2024 review in Nature Reviews Physics reports speed-ups of ten thousand to a hundred thousand times over conventional solvers.^[6] The catch: a surrogate only knows the situations it was trained on. More in What is AI-accelerated physics?

References

1. Newton project. Newton documentation: Solvers. 2026.
2. Google DeepMind. MuJoCo documentation: Computation. 2026.
3. NVIDIA. NVIDIA Warp documentation. 2026.
4. OpenCFD. OpenFOAM v2506 release notes. June 2025.
5. NVIDIA. PhysicsNeMo release 25.08. August 2025.
6. Azizzadenesheli et al., Nature Reviews Physics. Neural operators for accelerating scientific simulations and design. April 2024.

Every link was opened and checked in September 2026. Links open in a new tab.