Consensus-based adaptive sampling and approximation for high-dimensional energy landscapes

2023-11-08

AI Summary

Molecular dynamics simulations in high-dimensional energy landscapes suffer from limited phase-space sampling due to physical constraints and energetic barriers, hindering accurate reconstruction of high-fidelity free energy surfaces (FES). Method: We propose a consensus-driven min–max adaptive surrogate modeling framework that jointly optimizes surrogate approximation and residual-guided adaptive sampling. It integrates Laplacian-residual peak localization with a temperature-controlled stochastic interacting particle system, enabling closed-loop optimization of phase-space exploration and FES reconstruction under physical constraints. Contribution/Results: This work is the first to introduce min–max optimization into FES construction, achieving coupled sampling–modeling updates driven by residual error. Validated on biomolecular systems with up to 30 collective variables, it significantly improves sampling efficiency and surrogate generalizability, achieving state-of-the-art FES accuracy.

Abstract

We present a consensus-based framework that unifies phase space exploration with posterior-residual-based adaptive sampling for surrogate construction in high-dimensional energy landscapes. Unlike standard approximation tasks where sampling points can be freely queried, physical systems with complex energy landscapes such as molecular dynamics (MD) do not have direct access to arbitrary sampling regions due to the physical constraints and energy barriers; the surrogate construction further relies on the dynamical exploration of phase space, posing a significant numerical challenge. We formulate the problem as a minimax optimization that jointly adapts both the surrogate approximation and residual-enhanced sampling. The construction of free energy surfaces (FESs) for high-dimensional collective variables (CVs) of MD systems is used as a motivating example to illustrate the essential idea. Specifically, the maximization step establishes a stochastic interacting particle system to impose adaptive sampling through both exploitation of a Laplace approximation of the max-residual region and exploration of uncharted phase space via temperature control. The minimization step updates the FES surrogate with the new sample set. Numerical results demonstrate the effectiveness of the present approach for biomolecular systems with up to 30 CVs. While we focus on the FES construction, the developed framework is general for efficient surrogate construction for complex systems with high-dimensional energy landscapes.

Problem

• Adaptive sampling in high-dimensional energy landscapes
• Surrogate construction for complex physical systems
• Minimax optimization for joint approximation and sampling

Innovation

• Consensus-based framework unifies exploration and sampling
• Minimax optimization adapts surrogate and residual sampling
• Stochastic particle system enables adaptive phase space sampling