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1. Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved

   https://doi.org/10.1039/D0SM01019G  

   Wang, Shu; Ma, Zhan; Pan, Wenxiao (September 2020, Soft Matter)

   null (Ed.)

   We present data-driven coarse-grained (CG) modeling for polymers in solution, which conserves the dynamic as well as structural properties of the underlying atomistic system. The CG modeling is built upon the framework of the generalized Langevin equation (GLE). The key is to determine each term in the GLE by directly linking it to atomistic data. In particular, we propose a two-stage Gaussian process-based Bayesian optimization method to infer the non-Markovian memory kernel from the data of the velocity autocorrelation function (VACF). Considering that the long-time behaviors of the VACF and memory kernel for polymer solutions can exhibit hydrodynamic scaling (algebraic decay with time), we further develop an active learning method to determine the emergence of hydrodynamic scaling, which can accelerate the inference process of the memory kernel. The proposed methods do not rely on how the mean force or CG potential in the GLE is constructed. Thus, we also compare two methods for constructing the CG potential: a deep learning method and the iterative Boltzmann inversion method. With the memory kernel and CG potential determined, the GLE is mapped onto an extended Markovian process to circumvent the expensive cost of directly solving the GLE. The accuracy and computational efficiency of the proposed CG modeling are assessed in a model star-polymer solution system at three representative concentrations. By comparing with the reference atomistic simulation results, we demonstrate that the proposed CG modeling can robustly and accurately reproduce the dynamic and structural properties of polymers in solution. 

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2. Transfer learning of memory kernels for transferable coarse-graining of polymer dynamics

   https://doi.org/10.1039/D1SM00364J  

   Ma, Zhan; Wang, Shu; Kim, Minhee; Liu, Kaibo; Chen, Chun-Long; Pan, Wenxiao (June 2021, Soft Matter)

   null (Ed.)

   The present work concerns the transferability of coarse-grained (CG) modeling in reproducing the dynamic properties of the reference atomistic systems across a range of parameters. In particular, we focus on implicit-solvent CG modeling of polymer solutions. The CG model is based on the generalized Langevin equation, where the memory kernel plays the critical role in determining the dynamics in all time scales. Thus, we propose methods for transfer learning of memory kernels. The key ingredient of our methods is Gaussian process regression. By integration with the model order reduction via proper orthogonal decomposition and the active learning technique, the transfer learning can be practically efficient and requires minimum training data. Through two example polymer solution systems, we demonstrate the accuracy and efficiency of the proposed transfer learning methods in the construction of transferable memory kernels. The transferability allows for out-of-sample predictions, even in the extrapolated domain of parameters. Built on the transferable memory kernels, the CG models can reproduce the dynamic properties of polymers in all time scales at different thermodynamic conditions (such as temperature and solvent viscosity) and for different systems with varying concentrations and lengths of polymers. 

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3. A unified framework for data-driven construction of stochastic reduced models with state-dependent memory

   She, Zhiyuan; Lyu, Liyao; Lei, Huan (September 2025, arXivorg)

   We present a unified framework for the data-driven construction of stochastic reduced models with state-dependent memory for high-dimensional Hamiltonian systems. The method addresses two key challenges: (i) accurately modeling heterogeneous non-Markovian effects where the memory function depends on the coarse-grained (CG) variables beyond the standard homogeneous kernel, and (ii) efficiently exploring the phase space to sample both equilibrium and dynamical observables for reduced model construction. Specifically, we employ a consensus-based sampling method to establish a shared sampling strategy that enables simultaneous construction of the free energy function and collection of conditional two-point correlation functions used to learn the state-dependent memory. The reduced dynamics is formulated as an extended Markovian system, where a set of auxiliary variables, interpreted as non-Markovian features, is jointly learned to systematically approximate the memory function using only two-point statistics. The constructed model yields a generalized Langevin-type formulation with an invariant distribution consistent with the full dynamics. We demonstrate the effectiveness of the proposed framework on a two-dimensional CG model of an alanine dipeptide molecule. Numerical results on the transition dynamics between metastable states show that accurately capturing state-dependent memory is essential for predicting non-equilibrium kinetic properties, whereas the standard generalized Langevin model with a homogeneous kernel exhibits significant discrepancies. 

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4. Probing conformational properties of conjugated polymers in dilute solutions under variable solvent quality via coarse‐grained modeling

   https://doi.org/10.1002/pol.20230689  

   Li, Zhaofan; Wang, Yang; Ma, Guorong; Liao, Yangchao; Gu, Xiaodan; Xia, Wenjie (November 2023, Journal of Polymer Science)

   Abstract Conjugated polymers (CPs), characterized by rigid conjugation backbones and flexible peripheral side chains, hold significant promise in various organic optoelectronic applications. In this study, we employ coarse‐grained molecular dynamics (CG‐MD) simulations to investigate the intricate interplay of solvent quality, temperature, and chain architecture (e.g., side‐chain length and molecular mass) on the conformational behaviors of CPs in dilute solutions. Our research uncovers distinctive conformational behaviors under varying solvent conditions, highlighting the versatile nature of polymer chains, which can adopt extended configurations in good solvents and transition to aggregated states in poor solvents. Additionally, the mass scaling exponent , a robust structural descriptor, consistently described CPs behavior across diverse architectures and solvent conditions. Furthermore, our study shows that a CP with longer side‐chain exhibits improved solubility, which is further confirmed by experimental observations. Moreover, our analysis of the shape descriptor provided valuable insights into the symmetry and dimensionality of CPs under varying solvent conditions. These findings offer a comprehensive understanding of conformational behaviors of CPs in dilute solution, which are helpful in guiding the conformational design of polymer for specific applications. 

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5. Data-driven coarse-grained modeling of non-equilibrium systems

   https://doi.org/10.1039/D1SM00413A  

   Wang, Shu; Ma, Zhan; Pan, Wenxiao (July 2021, Soft Matter)

   null (Ed.)

   Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many applications. However, it usually experiences significantly altered dynamics due to loss of degrees of freedom upon coarse-graining. To establish CG models that can faithfully preserve dynamics, previous efforts mainly focused on equilibrium systems. In contrast, various soft matter systems are known to be out of equilibrium. Therefore, the present work concerns non-equilibrium systems and enables accurate and efficient CG modeling that preserves non-equilibrium dynamics and is generally applicable to any non-equilibrium process and any observable of interest. To this end, the dynamic equation of a CG variable is built in the form of the non-stationary generalized Langevin equation (nsGLE), where the two-time memory kernel is determined from the data of the auto-correlation function of the observable of interest. By embedding the nsGLE in an extended dynamics framework, the nsGLE can be solved efficiently to predict the non-equilibrium dynamics of the CG variable. To prove and exploit the equivalence of the nsGLE and extended dynamics, the memory kernel is parameterized in a two-time exponential expansion. A data-driven hybrid optimization process is proposed for the parameterization, which integrates the differential-evolution method with the Levenberg–Marquardt algorithm to efficiently tackle a non-convex and high-dimensional optimization problem. 

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