Lanyon AI

Formal verification for a computable universe. Building the future of scientific computing.

[Lanyon AI @lanyon_ai]

Over the coming days and weeks, Lanyon AI will be gradually coming out of stealth, and we're so excited to show you what we've been working on.

Here's a brief message from our CEO Jonathan Gorard (@getjonwithit) about the shape of things to come, and what we think it may mean for the future of science, math, and artificial intelligence. Link below 👇

[Lanyon AI @lanyon_ai]

Technical deep dive: https://t.co/KbgR9zAxIj

GitHub repo: https://t.co/remtTiZkEc

[Lanyon AI @lanyon_ai]

Read the technical details of yesterday’s GitHub drop on the advection-diffusion equation in the first of our “technical deep dives” from CTO Ammar Hakim: what exactly did Lanyon implement, what exactly did Lanyon prove, and how can the formally verified kernels then be used to run production simulations using Lanyon’s “/simulate” tool?

This post places a particular emphasis on the mathematical and algorithmic aspects of the implemented solver, and its formal verification - future posts will focus more upon the verification details themselves (including the various subtleties that occur when proving algebraic theorems in floating point arithmetic, and how we mitigate them).

This will be the first of many deep technical posts covering various details of Lanyon’s workflow, from mathematical formulation, to algorithm discovery, to computational implementation, to formal verification, to production simulation. We hope you enjoy it!

[Lanyon AI @lanyon_ai]

@esa_was_taken With any luck, about 2 weeks! We can do it right now - it's just going to take us a couple of weeks to get around to writing up a rigorous case study.

[Lanyon AI @lanyon_ai]

8,000 lines of formally verified simulation code. 10,000 lines of Lean 4 proof. Solved in 158 seconds.

Our agent, Lanyon, just one-shotted a formally verified solver for the linear advection, isotropic advection-diffusion, and full/anisotropic advection-diffusion equations, in up to 3D, with end-to-end proofs of correctness for every property.

This is the first end-to-end formally verified solver for the advection-diffusion equation, generated entirely autonomously (in seconds) using a new kind of scientific AI. Link to the GitHub (including real-time screencaps) below.

[Lanyon AI @lanyon_ai]

Announcement: https://t.co/ZFJpX5fjYK

[Lanyon AI @lanyon_ai]

Over the coming days and weeks, Lanyon AI will be gradually coming out of stealth, and we're so excited to show you what we've been working on.

Here's a brief message from our CEO Jonathan Gorard (@getjonwithit) about the shape of things to come, and what we think it may mean for the future of science, math, and artificial intelligence. Link below 👇