Bayesian selection for coarse-grained models of liquid water

The necessity for accurate and computationally efficient representations of water in atomistic simulations that can span biologically relevant timescales has born the necessity of coarse-grained (CG) modeling. Despite numerous advances, CG water models rely mostly on a-priori specified assumptions. How these assumptions affect the model accuracy, efficiency, and in particular transferability, has not been systematically investigated. Here we propose a data driven, comparison and selection for CG water models through a Hierarchical Bayesian framework. We examine CG water models that differ in their level of coarse-graining, structure, and number of interaction sites. We find that the importance of electrostatic interactions for the physical system under consideration is a dominant criterion for the model selection. Multi-site models are favored, unless the effects of water in electrostatic screening are not relevant, in which case the single site model is preferred due to its computational savings. The charge distribution is found to play an important role in the multi-site model's accuracy while the flexibility of the bonds/angles may only slightly improve the models. Furthermore, we find significant variations in the computational cost of these models. We present a data informed rationale for the selection of CG water models and provide guidance for future water model designs

Hierarchical multiscale materials modeling: Calibration, uncertainty quantification, and decision support

Computational material models help establish structure-property relationships by simulating properties, and are most effective when physically-based. The length and time scales of each simulation are constrained both by model type and computing power. Significant uncertainty can arise when models attempt to bridge across length and time scales, especially when using different model constructs. Hierarchical multiscale modeling (HMM) links models at different scales by informing parameters and form of higher scale models based on lower scale simulations, which can reduce uncertainty. The combination of diverse information sources in HMMs requires rigorous approaches to evaluate uncertainty propagation. In the pursuit of improved methods for empirical testing and development of model hierarchies, four approaches in which information is coordinated amongst multiple models are presented. (1) In a reconciled top-down and bottom-up approach, a likelihood-based model calibration method is proposed, and bcc Fe crystal plasticity (CP) is used to demonstrate the compatibility of information pathways. (2) A statistical volume element (SVE) ensemble-based homogenization scheme of two models of cartridge brass polycrystal plasticity is used to inform a Bammann-Chiesa-Johnson macroplasticity model with a local variation in parameters. The effects of SVE size and model form on the performance of the homogenization in bridging microstructure variability to macroscale uncertainty are explored. (3) A multiscale model development framework is outlined for the reduced order modeling of mesoscale variability in cartridge brass. The variability in SVE simulations is included with the results of a series of spherical microindentation experiments in a multiscale data collection. An initial study of the modeling involved in connecting the two length scales is performed. (4) In a CP-finite element method (FEM) based Materials Knowledge System model of -Ti, the influence of texture is considered. Texture is parameterized using generalized spherical harmonics. The CP-FEM model is used with polycrystalline SVE-ensembles to calibrate the MKS model across different textures, sampled according to an uncertainty reduction criterion. Results of the work suggest that data collection is an especially critical step in the formulation and deployment of hierarchical multiscale models. The use of bottom-up information in calibrating a multiscale model is shown to be susceptible to bias. A multiscale approach to coarse-grained simulations of polycrystals at the mesoscale is proposed. An approach to automating the data collection for a reduced-order model of microstructure sensitive response is shown to be competitive with manual data selection, prior to full optimization of the automated approach.Ph.D

An iterative Bayesian filtering framework for fast and automated calibration of DEM models

The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy. The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density. As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress–strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young’s modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The a priori particle configuration is obtained from 3D X-ray computed tomography images. The a posteriori expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials