morgenfryd

The aim of morgenfryd is to uncover the mathematical laws governing our world by automating the generation of explicit, verifiable, high-fidelity models of dynamical systems

The world today: Manually defined explicit represenations

Dynamical systems are modelled using explicitly defined equational systems generated manually by domain experts.

✅ The governing equations are well-known, verifiable and explainable. It is easy to extend systems and learnings transfer from one domain to another.

❌ Very time-consuming, cost-intensive and manual.

The world we are moving to: Implicitly learned representations

Taking advantage of large scale machine learning, models are now trained to replicate observed data. The governing equations are then unknown to us, they are instead implicitly learned - typically using diffussion models, neural ODEs or other deep learning approaches.

✅ Brute-force, automated and hugely scalable. Can be applied to a variety of systems without having to understand the underlying dynamics.

❌ Black box. No understanding of the governing dynamics and poor ability to extrapolate beyond training data. Little new knowledge of the fundamentals of the governing equations of the world are acquired and what is learned is not transferable between domains.

The future: Learned explicit representations

Using recent advances in reasoning capabilities we can combine the two above approaches to instead automate the generation of explicit governing equations. This allows us to get the best of both worlds.

✅ Automation, scale, explainability, verifiabilty, transfer of knowledge between domains and a chance to understand the governing equations of our world.