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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. 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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3. 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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4. Nonlinear Multiview Analysis: Identifiability and Neural Network-based Implementation

   https://doi.org/10.1109/SAM48682.2020.9104404  

   Lyu, Qi; Fu, Xiao (June 2020, 2020 IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM))

   Multiview analysis aims to extract common information from data entities across different domains (e.g., acoustic, visual, text). Canonical correlation analysis (CCA) is one of the classic tools for this problem, which estimates the shared latent information via linear transforming the different views of data. CCA has also been generalized to the nonlinear regime, where kernel methods and neural networks are introduced to replace the linear transforms. While the theoretical aspects of linear CCA are relatively well understood, nonlinear multiview analysis is still largely intuition-driven. In this work, our interest lies in the identifiability of shared latent information under a nonlinear multiview analysis framework. We propose a model identification criterion for learning latent information from multiview data, under a reasonable data generating model. We show that minimizing this criterion leads to identification of the latent shared information up to certain indeterminacy. We also propose a neural network based implementation and an efficient algorithm to realize the criterion. Our analysis is backed by experiments on both synthetic and real data. 

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5. Data assimilation in operator algebras

   https://doi.org/10.1073/pnas.2211115120  

   Freeman, David; Giannakis, Dimitrios; Mintz, Brian; Ourmazd, Abbas; Slawinska, Joanna (February 2023, Proceedings of the National Academy of Sciences)

   We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification. 

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