On the Connection Between Diffusion Models and Molecular Dynamics

Neural Network Potentials (NNPs) have emerged as a powerful tool for modelling atomic interactions with high accuracy and computational efficiency. Recently, denoising diffusion models have shown promise in NNPs by training networks to remove noise added to stable configurations, eliminating the need for force data during training. In this work, we explore the connection between noise and forces by providing a new, simplified mathematical derivation of their relationship. We also demonstrate how a denoising model can be implemented using a conventional MD software package interfaced with a standard NNP architecture. We demonstrate the approach by training a diffusion-based NNP to simulate a coarse-grained lithium chloride solution and employ data duplication to enhance model performance.

Physics-Informed Neural Networks for Discovering Localised Eigenstates in Disordered Media

The Schr\"{o}dinger equation with random potentials is a fundamental model for understanding the behaviour of particles in disordered systems. Disordered media are characterised by complex potentials that lead to the localisation of wavefunctions, also called Anderson localisation. These wavefunctions may have similar scales of eigenenergies which poses difficulty in their discovery. It has been a longstanding challenge due to the high computational cost and complexity of solving the Schr\"{o}dinger equation. Recently, machine-learning tools have been adopted to tackle these challenges. In this paper, based upon recent advances in machine learning, we present a novel approach for discovering localised eigenstates in disordered media using physics-informed neural networks (PINNs). We focus on the spectral approximation of Hamiltonians in one dimension with potentials that are randomly generated according to the Bernoulli, normal, and uniform distributions. We introduce a novel feature to the loss function that exploits known physical phenomena occurring in these regions to scan across the domain and successfully discover these eigenstates, regardless of the similarity of their eigenenergies. We present various examples to demonstrate the performance of the proposed approach and compare it with isogeometric analysis.