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One essential goal of constructing coarse-grained molecular dynamics (CGMD) models is to accurately predict nonequilibrium processes beyond the atomistic scale. While a CG model can be constructed by projecting the full dynamics onto a set of resolved variables, the dynamics of the CG variables can recover the full dynamics only when the conditional distribution of the unresolved variables is close to the one associated with the particular projection operator. In particular, the model's applicability to various nonequilibrium processes is generally unwarranted due to the inconsistency in the conditional distribution. Here, we present a data-driven approach for constructing CGMD models that retain certain generalization ability for nonequilibrium processes. Unlike the conventional CG models based on preselected CG variables (e.g., the center of mass), the present CG model seeks a set of auxiliary CG variables similar to the time-lagged independent component analysis to maximize the velocity correlation. This effectively minimizes the entropy contribution of unresolved variables and ensures the distribution under a broad range of nonequilibrium conditions approaches the one under equilibrium. Numerical results of a polymer melt system demonstrate the significance of this broadly overlooked metric for the model's generalization ability, and the effectiveness of the present CG model for predicting the complex viscoelastic responses under various nonequilibrium flows. 

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, 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. 

We propose a generative model-based framework for learning collective variables (CVs) that faithfully capture the individual metastable states of the fulldimensional molecular dynamics (MD) systems. Unlike most existing approaches based on various feature extraction strategies, the new framework transfers the exhausting efforts of feature selection into a generative task of reconstructing the full-dimensional probability density function (PDF) from a set of CVs under a prior distribution with pre-assigned local maxima. By pairing the CVs with a set of auxiliary Gaussian random variables, we seek an invertible mapping that recovers the full-dimensional PDF and meanwhile, preserves the correspondence between the metastable states of the MD space and individual local maxima of the prior distribution. Through identifying the metastable states within MD space that are generally unknown and imposing the correspondence between the two spaces, the constructed CVs retain clear physical interpretations and provide kinetic insight for the molecular systems on the collective scale. We demonstrate the effectiveness of the proposed method with the alanine dipeptide in the aqueous environment. The constructed CVs faithfully capture the essential metastable states of the full MD systems, which show good agreement with kinetic properties such as the transition from the ballistic to the plateau regime for the mean square displacement. 

A hallmark of meso-scale interfacial fluids is the multi-faceted, scale-dependent interfacial energy, which often manifests different characteristics across the molecular and continuum scale. The multi-scale nature imposes a challenge to construct reliable coarse-grained (CG) models, where the CG potential function needs to faithfully encode the many-body interactions arising from the unresolved atomistic interactions and account for the heterogeneous density distributions across the interface. We construct the CG models of both single- and two-component polymeric fluid systems based on the recently developed deep coarse-grained potential [Zhang et al., J. Chem. Phys. 149, 034101 (2018)] scheme, where each polymer molecule is modeled as a CG particle. By only using the training samples of the instantaneous force under the thermal equilibrium state, the constructed CG models can accurately reproduce both the probability density function of the void formation in bulk and the spectrum of the capillary wave across the fluid interface. More importantly, the CG models accurately predict the volume-to-area scaling transition for the apolar solvation energy, illustrating the effectiveness to probe the meso-scale collective behaviors encoded with molecular-level fidelity.