# Molecular Learning Dynamics

arXiv: https://arxiv.org/abs/2504.10560 · HTML: https://mlsanity.com/paper/2504.10560/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 14 Apr 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Orb: A Fast, Scalable Neural Network Potential](https://mlsanity.com/paper/2410.22570/) (2024)
- [The world as a neural network](https://mlsanity.com/paper/2008.01540/) (2020)
- [Towards a Theory of Evolution as Multilevel Learning](https://mlsanity.com/paper/2110.14602/) (2021)
- [Towards a theory of machine learning](https://mlsanity.com/paper/2004.09280/) (2020)
- [Towards a theory of quantum gravity from neural networks](https://mlsanity.com/paper/2111.00903/) (2021)
- [The Autodidactic Universe](https://mlsanity.com/paper/2104.03902/) (2021)
- [Thermodynamics of Evolution and the Origin of Life](https://mlsanity.com/paper/2110.15066/) (2021)
- [Dataset-learning duality and emergent criticality](https://mlsanity.com/paper/2405.17391/) (2024)
- [Emergent field theories from neural networks](https://mlsanity.com/paper/2411.08138/) (2024)
- [Autonomous particles](https://mlsanity.com/paper/2301.10077/) (2023)
- [Covariant Gradient Descent](https://mlsanity.com/paper/2504.05279/) (2025)

## Built on by (most cited first, 1 of 1)

- [Geometric Learning Dynamics](https://mlsanity.com/paper/2504.14728/) (2025)

## Abstract (arXiv)

We apply the physics-learning duality to molecular systems by complementing the physical description of interacting particles with a dual learning description, where each particle is modeled as an agent minimizing a loss function. In the traditional physics framework, the equations of motion are derived from the Lagrangian function, while in the learning framework, the same equations emerge from learning dynamics driven by the agent loss function. The loss function depends on scalar quantities that describe invariant properties of all other agents or particles. To demonstrate this approach, we first infer the loss functions of oxygen and hydrogen directly from a dataset generated by the CP2K physics-based simulation of water molecules. We then employ the loss functions to develop a learning-based simulation of water molecules, which achieves comparable accuracy while being significantly more computationally efficient than standard physics-based simulations.