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Full-Text Articles in Physical Sciences and Mathematics
Spatial Multi-Level Interacting Particle Simulations And Information Theory-Based Error Quantification, Evangelia Kalligiannaki, Markos Katsoulakis, Petr Plechac
Spatial Multi-Level Interacting Particle Simulations And Information Theory-Based Error Quantification, Evangelia Kalligiannaki, Markos Katsoulakis, Petr Plechac
Markos Katsoulakis
We propose a hierarchy of two-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution levels, taking advantage of the low sampling cost in a coarse space and developing local reconstruction strategies from coarse-grained dynamics. Furthermore, a natural extension to a multilevel kinetic coarse-grained Monte Carlo is presented. Microscopic reconstruction corrects possibly significant errors introduced through coarse-graining, leading to the controlled-error approximation of the sampled stochastic process. In this manner, the proposed algorithm overcomes known shortcomings of coarse-graining of particle systems with complex …
Information-Theoretic Tools For Parametrized Coarse-Graining Of Non-Equilibrium Extended Systems, Markos Katsoulakis, Petr Plechac
Information-Theoretic Tools For Parametrized Coarse-Graining Of Non-Equilibrium Extended Systems, Markos Katsoulakis, Petr Plechac
Markos Katsoulakis
In this paper, we focus on the development of new methods suitable for efficient and reliable coarse-graining of non-equilibrium molecular systems. In this context, we propose error estimation and controlled-fidelity model reduction methods based on Path-Space Information Theory, combined with statistical parametric estimation of rates for non-equilibrium stationary processes. The approach we propose extends the applicability of existing information-based methods for deriving parametrized coarse-grained models to Non-Equilibrium systems with Stationary States. In the context of coarse-graining it allows for constructing optimal parametrized Markovian coarse-grained dynamics within a parametric family, by minimizing information loss (due to coarse-graining) on the path space. …
A Relative Entropy Rate Method For Path Space Sensitivity Analysis Of Stationary Complex Stochastic Dynamics, Yannis Pantazis, Markos Katsoulakis
A Relative Entropy Rate Method For Path Space Sensitivity Analysis Of Stationary Complex Stochastic Dynamics, Yannis Pantazis, Markos Katsoulakis
Markos Katsoulakis
We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the relative entropy rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the relative entropy rate and the corresponding Fisher information matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-Gaussian stationary probability …