Why is fusion hard? In the first in our series of “physics deep dives”, Chief Scientist @JunoRavin shows how Lanyon can be used to autonomously rediscover and analyze some of the fundamental physics difficulties underlying magnetic confinement fusion: the sausage instability that killed the Z-pinch device, and the interchange/flute instabilities that continue to plague magnetic mirror devices. This deep dive shows the true power of Lanyon’s neurosymbolic architecture for applied physics research, combining formally verified 3D MHD simulations produced by Lanyon’s symbolic layer, with highly flexible AI-driven physics analyses enabled by Lanyon’s neural layer. Stay tuned for further additions to this series, where we will dive deeper into field-reversed configurations, tokamaks, stellarators, and all of the new physics difficulties that emerge at these new ranges of timescales. Post below 👇

Using Lanyon to autonomously discover and verify new models and algorithms for continuum mechanics. Simulating high-energy impact of a copper projectile on an elastoplastic plate, plus the resulting damage profile. The discovered model matches the experimental value for the effective plastic strain to within 5%. Model discovery, formal verification, software implementation, and numerical simulation all completed in less than 5 minutes, from a single prompt.

It’s our pleasure to welcome Andrew "Tasman" Powis to the Lanyon AI team as Founding Member of Technical Staff, specializing in AI model development and advanced numerical algorithms. Tasman joins us from the Princeton Plasma Physics Laboratory and brings deep expertise in artificial intelligence, algorithm design, and high-performance computing, with a particular interest in kinetic simulations, spacecraft propulsion and semiconductor manufacturing. Welcome Tasman!

It’s our pleasure to welcome Aanya Bhandari to the Lanyon AI team as a Research Fellow, specializing in frontier model architecture and training. Aanya joins us following a research fellowship at Princeton University working with our CEO Jonathan Gorard on formal verification for transformer and recurrent neural network architectures. She brings expertise in frontier AI architectures, financial technology, and quantum computing. Welcome Aanya!

Rapidly outgrowing our dinky little Princeton office…

It’s our pleasure to welcome Chris Rugenstein to the Lanyon AI team as Founding Member of Technical Staff, specializing in type systems and formal verification. Chris joins us from the Institute for Defense Analyses and the Department of Energy, and brings deep expertise in pure mathematics, theoretical computer science, and formal methods for type theory. Welcome Chris!

A few words from @getjonwithit on the meaning of the present moment, and what a human-oriented outlook for science, mathematics, and technology may look like in a world of growing AI capabilities. lanyon.ai/blog/vision/

An electromagnetic wavepacket diffracting over a metal cylinder inside a metal waveguide. Simulated using a high-order (p=2) discontinuous Galerkin scheme for the perfectly hyperbolic Maxwell equations, autonomously discovered, verified, and implemented with Lanyon.

We've been having a lot of fun using Lanyon to perform automated discovery of new discontinuous Galerkin (DG) algorithms for discretizing PDEs. We're starting with simple linear and nonlinear advection problems, with some more advanced (and exciting!) examples on the way. The workflow is simple: have Lanyon autonomously explore the space of possible modal DG discretizations (of any order of accuracy), while autonomously checking its work by attempt to prove various correctness properties of the modal reconstruction polynomials, surface terms, and volume integrals, as well as entropy stability properties of the underlying fluxes. Once Lanyon finds a new discretization that works, it generates an optimized implementation in C and starts autonomously running numerical simulations with it. It turns out that you can very quickly discover all kinds of weird and wonderful (but provably correct!) numerical algorithms this way, many of which go beyond the current state of the art. And we're only just scratching the surface of what is possible with formally verified numerics. Even for these simple cases, the optimized implementations (for p=1 and p=2, i.e. second-order and third-order accuracy) span around 30,000 lines of generated C code and around 40,000 lines of generated Lean proof. But Lanyon completes the whole algorithm discovery task in a few minutes, and with less than a dollar in total inference cost. We've updated our Research Notes with some of these new algorithmic results, but stay tuned for more discoveries still to come. GitHub links and Research Notes below. 👇

Building a formal verification framework for physics and engineering. A talk by our CEO Jonathan Gorard (@getjonwithit) from March 2025 at Princeton, outlining the beginnings of Lanyon, and the challenges of formally verifying numerical methods: youtube.com/watch?v=8NDcltA5…

Full 3D simulation of stellar wind impacting a planetary magnetosphere (with a weak dipole field). Simulation one-shot with Lanyon, with end-to-end formal verification, via a single prompt, in <2 minutes. We see a magnetic pressure cavity, dragging of the dipole field, and the formation of a nightside current sheet.

Formally verified magnetohydrodynamics, with provably hyperbolicity-preserving magnetic divergence error correction. Simulating plasma vortices and supersonic plasma flows in arbitrary geometries using shock-capturing schemes for the equations of ideal MHD, all implemented and verified autonomously with Lanyon. ~32,000 lines of C, ~50,000 lines of Lean proof, ~150 correctness theorems, all generated in ~7 minutes. The ideal MHD equations couple the equations of hydrodynamics with Maxwell’s equations for electromagnetism to describe the interactions of perfectly conducting fluids with magnetic fields. As an elegant reduced-order description, the ideal MHD equations occur ubiquitously throughout heliophysics, geophysics, and astrophysical plasma physics, as well as in modeling the equilibrium and stability of nuclear fusion reactors. Solving these equations involves unique numerical and algorithmic challenges, including issues surrounding the preservation of divergence constraints for the magnetic field, as well as complex thermodynamic stability and wave-speed restrictions. Lanyon one-shotted an end-to-end formally verified solver for the ideal MHD equations, including a provably hyperbolicity-preserving divergence correction scheme based on the Dedner et al. approach, with fully executable mathematical, physical, and numerical correctness proofs. Then it ran a variety of complex numerical and physical validation simulations, and autonomously analyzed the results. To the best of our knowledge, this is the first ever fully formally verified divergence correction scheme for the MHD equations. GitHub link and technical deep dive below.👇