# Follow the MEP: Scalable Neural Representations for Minimum-Energy Path Discovery in Molecular Systems

arXiv: https://arxiv.org/abs/2504.16381 · HTML: https://mlsanity.com/paper/2504.16381/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 61 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 12 of 12)

- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Optimal approximation of piecewise smooth functions using deep ReLU neural networks](https://mlsanity.com/paper/1709.05289/) (2017)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [Action Matching: Learning Stochastic Dynamics from Samples](https://mlsanity.com/paper/2210.06662/) (2022)
- [Scalable Optimization in the Modular Norm](https://mlsanity.com/paper/2405.14813/) (2024)
- [Generative Modeling of Molecular Dynamics Trajectories](https://mlsanity.com/paper/2409.17808/) (2024)
- [A Computational Framework for Solving Wasserstein Lagrangian Flows](https://mlsanity.com/paper/2310.10649/) (2023)
- [Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths](https://mlsanity.com/paper/2207.02149/) (2022)
- [Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling](https://mlsanity.com/paper/2410.07974/) (2024)
- [Geometric Trajectory Diffusion Models](https://mlsanity.com/paper/2410.13027/) (2024)
- [Implicit Neural Representations for Chemical Reaction Paths](https://mlsanity.com/paper/2502.15843/) (2025)

## Abstract (arXiv)

Characterizing conformational transitions in physical systems remains a fundamental challenge, as traditional sampling methods struggle with the high-dimensional nature of molecular systems and high-energy barriers between stable states. These rare events often represent the most biologically significant processes, yet may require months of continuous simulation to observe. One way to understand the function and mechanics of such systems is through the minimum energy path (MEP), which represents the most probable transition pathway between stable states in the high-friction, low-temperature limit. We present a method that reformulates MEP discovery as a fast and scalable neural optimization problem. By representing paths as implicit neural representations and training with differentiable molecular force fields, our method discovers transition pathways without expensive sampling. Our approach scales to large biomolecular systems through a simple loss function derived from the path's likelihood via the Onsager-Machlup action and a scalable new architecture, AdaPath. We demonstrate this approach on two proteins, including an explicitly hydrated BPTI system with more than 3,500 atoms. Our method identifies a MEP that captures the same conformational change observed in a millisecond-scale molecular dynamics (MD) simulation in just minutes on a standard GPU, rather than weeks on a specialized cluster.