A unified framework for data-driven construction of stochastic reduced models with state-dependent memory
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915485787881472 |
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| author | She, Zhiyuan Lyu, Liyao Smith, Bryan Ronain Lei, Huan |
| author_facet | She, Zhiyuan Lyu, Liyao Smith, Bryan Ronain Lei, Huan |
| contents | 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: (\rmnum{1}) accurately modeling heterogeneous non-Markovian effects where the memory function depends on the coarse-grained (CG) variables beyond the standard homogeneous kernel, and (\rmnum{2}) 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A unified framework for data-driven construction of stochastic reduced models with state-dependent memory She, Zhiyuan Lyu, Liyao Smith, Bryan Ronain Lei, Huan Computational Physics 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: (\rmnum{1}) accurately modeling heterogeneous non-Markovian effects where the memory function depends on the coarse-grained (CG) variables beyond the standard homogeneous kernel, and (\rmnum{2}) 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. |
| title | A unified framework for data-driven construction of stochastic reduced models with state-dependent memory |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2509.07264 |