03 / Research notes
Research from the
Lanyon Team
Technical deep dives from the Lanyon team on formal verification, numerical methods, scientific AI, and computational physics.
Benchmarking · 14 min
Benchmarking Lanyon against Frontier Models: Nonlinear PDEs
In this technical deep dive, we extend previous benchmarking by comparing the current frontier models against Lanyon in terms of accuracy and cost for the solutions to *nonlinear* partial differential equations.
Numerical methods · 23 min
The Euler Equations of Gas Dynamics
In this deep dive we study the Euler equations. These are a fundamental set of equations that describe inviscid fluid flow. They also form the basis of the Navier-Stokes equations.
Numerical methods · 18 min
General Relativistic Electrodynamics
In this deep dive we look at the general relativistic extension of Maxwell's equations to the curved spacetimes around black holes and other extreme environments.
Numerical methods · 13 min
The Burgers Equation
We study the simplest nonlinear scalar hyperbolic PDE, the Burgers Equation, and show how shocks and rarefaction waves form.
Benchmarking · 18 min
Benchmarking Lanyon against Frontier Models: Linear PDEs
In this technical deep dive, we compare the current frontier models against Lanyon in terms of accuracy and cost for the solutions to linear partial differential equations.
Numerical methods · 21 min
The Maxwell Equations of Electromagnetism
In this numeric deep-dive we look closely at the structure and properties of Maxwell equations and show some examples of Lanyon generated proofs and simulations.
Numerical methods · 15 min
The Advection-Diffusion Equation
In this numerics deep dive we look at a fundamental equation of mathematical physics: the advection-diffusion equation.
Numerical methods · 23 min
A Grimoire of Definitions, Identities, Equation Systems, and all That
This research note aims to collect properties of classes of equations that Lanyon can solve, especially those for which our neurosymbolic system generates formal proofs of correctness.
Numerical methods · In preparation
The Equations of Ideal Magnetohydrodynamics
A ubiquitous system of equations, describing the behaviors of perfectly electrically-conducting fluids interacting with magnetic fields.