GradNav: Accelerated Exploration of Potential Energy Surfaces with Gradient-Based Navigation

TL;DR

GradNav introduces a physics-preserving, observation-density-gradient-guided restart strategy to accelerate exploration of molecular PESs and escape deep wells. It uses two nested loops to update simulation starting points via the gradient of observation density, enabling rapid discovery of metastable states without biasing physical parameters. Across Müller and modified Müller potentials and Fs-Peptide MD data, GradNav achieves faster deep-well escape (lower DWEF) and reduced initialization sensitivity (higher SSIR), while enabling more complete PES reconstruction. The approach offers a practical, data-driven means to obtain richer conformational landscapes and can potentially enhance latent-space exploration in machine learning frameworks for molecular systems.

Abstract

The exploration of molecular systems' potential energy surface is important for comprehending their complex behaviors, particularly through identifying various metastable states. However, the transition between these states is often hindered by substantial energy barriers, demanding prolonged molecular simulations that consume considerable computational efforts. Our study introduces the GradNav algorithm, which enhances the exploration of the energy surface, accelerating the reconstruction of the potential energy surface (PES). This algorithm employs a strategy of initiating short simulation runs from updated starting points, derived from prior observations, to effectively navigate across potential barriers and explore new regions. To evaluate GradNav's performance, we introduce two metrics: the deepest well escape frame (DWEF) and the search success initialization ratio (SSIR). Through applications on Langevin dynamics within Mueller-type potential energy surfaces and molecular dynamics simulations of the Fs-Peptide protein, these metrics demonstrate GradNav's enhanced ability to escape deep energy wells, as shown by reduced DWEF values, and its reduced reliance on initial conditions, highlighted by increased SSIR values. Consequently, this improved exploration capability enables more precise energy estimations from simulation trajectories.

Figures (11)

• Figure 1: Overview of the GradNav Algorithm. a Illustration of the update rule: the update rate is increased if the centroid of the subsequent trajectory falls within the previously determined boundary. This process repeats until a new potential well is identified. b Flowchart detailing the steps of the GradNav algorithm.
• Figure 2: Trajectories generated using Langevin Dynamics (LD) and the GradNav algorithm, starting from the deepest valley.
• Figure 3: Simulation starting point updates. Upper panels display results from Müller potential, while lower panels feature results from modified Müller potential. Panels a and c (left) demonstrate updates from the end of one run to the start of the next, marked by arrows. Panels b and d (right) show how update rates change across inner loop iterations and reset to zero when a new well is found. For clarity, updates from the first 5,000 frames are depicted.
• Figure 4: Count of successful potential well identifications by initial position. The left panels, a and c, depict the results obtained using Langevin dynamics (LD). In contrast, the right panels, b and d, illustrate the outcomes derived from GradNav.
• Figure 5: Boltzmann distribution of trajectories. The left panels depict results from the Müller potential and the right panels from the modified Müller potential. Panels a and b show trajectories on the energy cross-section. Panels c and d present the distribution histogram of trajectories. Panels e and f illustrate energy estimates derived using the Boltzmann distribution equation. The energy of state $i$, denoted as $\varepsilon_i$, is represented by $E(\mathbf{X})$ within the energy surface.