Path-space variational inference for non-equilibrium coarse-grained systems

Abstract: In this paper, we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular dynamics. The latter are ubiquitous in physicochemical and biological applications, where they are typically associated with coupling mechanisms, multi-physics and/or boundary conditions. In general the non-equilibrium steady states are not known explicitly as they do not necessarily have a Gibbs structure. The presented approach can compare microscopic behavior of molecular systems to parametric and non-parametric coarse-grained one using the relative entropy between distributions on the path space and setting up a corresponding path space variational inference problem. The methods can become entirely data-driven when the microscopic dynamics are replaced with corresponding correlated data in the form of time series. Furthermore, we present connections and generalizations of force matching methods in coarse-graining with path-space information methods, as well as demonstrate the enhanced transferability of information-based parameterizations to general observables due to information inequalities. We further discuss methodological connections between information-based coarse-graining of molecular systems and variational inference methods primarily developed in the machine learning community. However, we note that the work presented here addresses variational inference for correlated time series due to the focus on dynamics. The applicability of the proposed methods is demonstrated on high-dimensional stochastic processes given by Langevin, overdamped and driven Langevin dynamics of interacting particles.

• The paper presents a framework that minimizes relative entropy over path distributions to derive coarse-grained models from microscopic dynamics.
• It applies an information-theoretic approach to effectively model non-equilibrium systems beyond traditional equilibrium methods.
• The method enhances model transferability across observables and states using data-driven stochastic optimization techniques.

Path-space Variational Inference for Non-equilibrium Coarse-grained Systems

The paper "Path-space variational inference for non-equilibrium coarse-grained systems" presents a framework for efficiently deriving coarse-grained molecular models from microscopic dynamics using path-space variational inference. This approach contrasts traditional force-matching or structure-based methods and offers a unified framework for both equilibrium and non-equilibrium systems. Through an information-theoretic lens, the authors demonstrate that optimized coarse-grained models can be derived entirely from dynamic data, resulting in enhanced model transferability across different observables.

Information-theoretic Approach

Relative Entropy in Coarse-graining

The central concept explored in the paper is the use of relative entropy as a metric to compare coarse-grained models with their microscopic counterparts. By minimizing the relative entropy between path-space distributions of coarse-grained and microscopic simulations, the framework establishes an optimal parameterization for coarse-grained models. Unlike traditional methods limited to equilibrium systems, this approach is versatile and directly applicable to non-equilibrium systems without relying on Gibbs state assumptions.

Path-space Variational Inference

Path space variational inference involves setting up an optimization problem that minimizes the relative entropy over the path distributions, offering a principled way to quantify discrepancies between coarse-grained and microscopic dynamics. This process relates closely to machine learning techniques wherein variational inference optimizes a parametric model to be close to a target distribution.

Data-driven Optimization

The paper posits that coarse-grained models can be structured to maximize the information content derived from dynamic data using path-space analysis. This enables effective utilization of simulation data without explicit knowledge of the underlying microscopic model's distributions, thereby promoting the applicability in data-driven settings.

Applications and Implications

Non-equilibrium Systems

A notable advancement is the applicability of this method to non-equilibrium computational models. Traditional coarse-graining methods are often inadequate for systems not possessing a Gibbs structure or detailed balance. By leveraging path-space metrics, the presented framework effectively overcomes these limitations, making it powerful for a wide range of physical and biological applications where non-equilibrium conditions commonly occur.

Enhanced Transferability

The use of information-based metrics demonstrates enhanced transferability of coarse-grained models across different observables and thermodynamic states. This feature is achieved without re-parametrization, as the relative entropy inherently quantifies the discrepancy across path-space measures universally.

Practical Implementation

Applications of these methods span high-dimensional stochastic processes, articulated in the form of effective Langevin and overdamped Langevin dynamics. Computational strategies, including stochastic optimization techniques, are employed to efficiently approximate the fine-scale dynamics using coarse-grained stochastic models.

Conclusion

The paper introduces an advanced methodological framework for deriving coarse-grained models based on path-space variational inference, applicable to both equilibrium and non-equilibrium systems. Utilizing information-theoretic metrics, the approach addresses significant challenges in multi-scale modeling by offering unified tools for model optimization directly from dynamic data. The strong implications for computational techniques across various domains establish this as a crucial advancement in the fine-scale to coarse-scale modeling transferability, with prospects for even broader applications in machine learning and AI-driven modeling.