Related papers: Coarse-graining molecular dynamics models using an…

We propose a robust, adaptive coarse-grid correction scheme for matrix-free geometric multigrid targeting PDEs with strongly varying coefficients. The method combines uniform geometric coarsening of the underlying grid with heterogeneous…

We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical…

In this paper, we show how kernel-based models for the Koopman generator -- the gEDMD method -- can be used to identify coarse-grained dynamics on reduced variables, which retain the slowest transition timescales of the original dynamics.…

A careful derivation of the generalized Langevin equation using "Zwanzig flavor" projection operator formalism is presented. We provide arguments why this formalism has better properties compared to alternative projection-operator…

In many far-from-equilibrium biological systems, energy injected by irreversible processes at microscopic scales propagates to larger scales to fulfill important biological functions. But given dissipative dynamics at the microscale, how…

Coarse-grained (CG) modeling has gained significant attention in recent years due to its wide applicability in enhancing the spatiotemporal scales of molecular simulations. While CG simulations, often performed with Hamiltonian mechanics,…

A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variables are not slow in general but they satisfy an overdamped…

We present a derivation of a coarse-grained model from the Langevin dynamics. The focus is placed on the memory kernel function and the fluctuation-dissipation theorem. Also presented is an hierarchy of approximations for the memory and…

By exact projection in phase space we derive the generalized Langevin equation (GLE) for time-filtered observables. We employ a general convolution filter that directly acts on arbitrary phase-space observables and can involve low-pass,…

We propose a highly coarse-grained simulation model for crystalline polymer solids with crystalline lamellar structures. The mechanical properties of a crystalline polymer solid are mainly determined by the crystalline lamellar structures.…

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes,…

Many approaches of coarse-graining have been developed under the names of Cosserat theory or polar-fluid theory, for those materials in which some component elements undergo non-affine deformations, such as elastic materials with inclusions…

We present a multiscale continuous Galerkin (MSCG) method for the fast and accurate stochastic simulation and optimization of time-harmonic wave propagation through photonic crystals. The MSCG method exploits repeated patterns in the…

Quantum geometrical molecular dynamics provides a quantum geometric picture for understanding reactive dynamics, especially excited-state conical intersection dynamics, and also a numerically exact method for strongly correlated…

We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with…

Conjugated organic molecules play a central role in a wide range of optoelectronic devices, including organic light-emitting diodes, organic field-effect transistors, and organic solar cells. A major bottleneck in the computational design…

Efficient sampling of the Boltzmann distribution of molecular systems is a long-standing challenge. Recently, instead of generating long molecular dynamics simulations, generative machine learning methods such as normalizing flows have been…

We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…

We formulate a new projection-based reduced-ordered modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov-Galerkin (APG) method, is derived by decomposing the generalized…

We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms) and atomistic simulations of the Larson model of micelle…