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Predictions of complex systems ranging from natural language processing to weather forecasting have benefited from advances in Recurrent Neural Networks (RNNs). RNNs are typically trained using techniques like Backpropagation Through Time (BPTT) to minimize one-step-ahead prediction loss. During testing, RNNs often operate in an auto-regressive mode, with the output of the network fed back into its input. However, this process can eventually result in exposure bias since the network has been trained to process "ground-truth" data rather than its own predictions. This inconsistency causes errors that compound over time, indicating that the distribution of data used for evaluating losses differs from the actual operating conditions encountered by the model during training. Inspired by the solution to this challenge in language processing networks we propose the Scheduled Autoregressive Truncated Backpropagation Through Time (BPTT-SA) algorithm for predicting complex dynamical systems using RNNs. We find that BPTT-SA effectively reduces iterative error propagation in Convolutional and Convolutional Autoencoder RNNs and demonstrates its capabilities in the long-term prediction of high-dimensional fluid flows. [Display omitted] • RNNs trained with teacher forcing (TF) suffer from the exposure bias effect • Exposure bias is the incosistentcy between TF training and autoregressive inference • Scheduled Autoregressive BPTT (BPTT-SA) alleviates the exposure bias effect • We employ BPTT-SA for long-term forecasting of the Navier-Stokes flow past a cylinder • BPTT-SA improves long-term forecasting accuracy for CNN-RNNs, and Conv-RNNs [ABSTRACT FROM AUTHOR]

Abstract: We present a novel particle method, combining remeshed Smoothed Particle Hydrodynamics with Immersed Boundary and Level Set techniques for the simulation of flows past complex deforming geometries. The present method retains the Lagrangian adaptivity of particle methods and relies on the remeshing of particle locations in order to ensure the accuracy of the method. In fact this remeshing step enables the introduction of Immersed Boundary Techniques used in grid based methods. The method is applied to simulations of flows of isothermal and compressible fluids past steady and unsteady solid boundaries that are described using a particle Level Set formulation. The method is validated with two and three-dimensional benchmark problems of flows past cylinders and spheres and it is shown to be well suited to simulations of large scale simulations using tens of millions of particles, on flow-structure interaction problems as they pertain to self-propelled anguilliform swimmers. [Copyright &y& Elsevier]

We present a convergence study for a hybrid Lattice Boltzmann-Molecular Dynamics model for the simulation of dense liquids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The velocity field from the atomistic domain is introduced as forcing terms to the Lattice Boltzmann model of the continuum while the mean field of the continuum imposes mean field conditions for the atomistic domain. In the present paper we investigate the effect of varying the size of the atomistic subdomain in simulations of two dimensional flows of liquid argon past carbon nanotubes and assess the efficiency of the method. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a computationally efficient, two-dimensional, feature point tracking algorithm for the automated detection and quantitative analysis of particle trajectories as recorded by video imaging in cell biology. The tracking process requires no a priori mathematical modeling of the motion, it is self-initializing, it discriminates spurious detections, and it can handle temporary occlusion as well as particle appearance and disappearance from the image region. The efficiency of the algorithm is validated on synthetic video data where it is compared to existing methods and its accuracy and precision are assessed for a wide range of signal-to-noise ratios. The algorithm is well suited for video imaging in cell biology relying on low-intensity fluorescence microscopy. Its applicability is demonstrated in three case studies involving transport of low-density lipoproteins in endosomes, motion of fluorescently labeled Adenovirus-2 particles along microtubules, and tracking of quantum dots on the plasma membrane of live cells. The present automated tracking process enables the quantification of dispersive processes in cell biology using techniques such as moment scaling spectra. [Copyright &y& Elsevier]

The article informs that the cost of optimizing expensive problems is dominated by the number of fitness function evaluations required to reach an acceptable solution. For evolutionary algorithms, various approaches exist to reduce this cost by exploiting knowledge of the history of evaluated points. This knowledge can for instance be used to adapt the recombination and mutation operators in order to sample offspring in a promising areas. Knowledge of past evaluations can also be used to build an empirical model that approximates the fitness function to optimize. The approximation is then used to predict promising new solutions at a smaller evaluation cost than the original problem. The prediction quality generally improves with a growing number of evaluated points in the optimization process.

Presents information on a study which examined the sub-critical evaporation of a nanometer-size droplet using molecular dynamics simulation. Outline of the numerical method that includes the description of the applied tree data structure and of the heating algorithm; Convergence study and the predicted evaporation rates.

The article discusses the study concerning the hydrodynamics of anguilliform swimming motions using three-dimensional simulations of the fluid flow past a self-propelled body. To determine the motion of the body for different objectives, an evolutionary optimization algorithm was used, linking swimming motion and biological function in a systematic fashion.

Mathematical models can support the drug development process by predicting the pharmacokinetic (PK) properties of the drug and optimal dosing regimens. We have developed a pharmacokinetic model that includes a biochemical molecular interaction network linked to a whole-body compartment model. We applied the model to study the PK of the anti-vascular endothelial growth factor (VEGF) cancer therapeutic agent, aflibercept. Clinical data is used to infer model parameters using a Bayesian approach, enabling a quantitative estimation of the contributions of specific transport processes and molecular interactions of the drug that cannot be examined in other PK modeling, and insight into the mechanisms of aflibercept's antiangiogenic action. Additionally, we predict the plasma and tissue concentrations of unbound and VEGF-bound aflibercept. Thus, we present a computational framework that can serve as a valuable tool for drug development efforts. [ABSTRACT FROM AUTHOR]

We present nonequilibrium molecular dynamics simulations of the flow of liquid–vapour water mixtures and mixtures of water and nitrogen inside carbon nanotubes. A new adaptive forcing scheme is proposed to impose a mean flow through the system. The flow of liquid water is characterised by a distinct layering of the water molecules in the vicinity of the boundary and a slip length that is found to increase with the radius of the carbon nanotube. Increasing the temperature and pressure of the system furthermore results in a decrease in the slip length. For the flow of mixtures of nitrogen and water we find that the slip length is reduced as compared to the slip for the pure water. The shorter slip length is attributed to the fact that nitrogen forms droplets at the carbon surface, thus partially shielding the bulk flow from the hydrophobic carbon surface. [Copyright &y& Elsevier]

We present an extension of the classical scheme of smoothed particle hydrodynamics (SPH) for the accurate handling of diffusion terms in the momentum and energy equation of viscous and heat conducting flows. A key aspect of the present SPH approach is the periodic reinitialization (remeshing) of the particle locations, which are being distorted by the flow map. High-order moment conserving kernels are being implemented for this remeshing procedure leading to accurate simulations. The accuracy of the proposed SPH methodology is tested for a number of benchmark problems involving flow and energy transport. The results demonstrate that the proposed SPH methodology is capable of DNS quality simulations while maintaining its robustness and adaptivity. [Copyright &y& Elsevier]

We examine the efficiency of Recurrent Neural Networks in forecasting the spatiotemporal dynamics of high dimensional and reduced order complex systems using Reservoir Computing (RC) and Backpropagation through time (BPTT) for gated network architectures. We highlight advantages and limitations of each method and discuss their implementation for parallel computing architectures. We quantify the relative prediction accuracy of these algorithms for the long-term forecasting of chaotic systems using as benchmarks the Lorenz-96 and the Kuramoto–Sivashinsky (KS) equations. We find that, when the full state dynamics are available for training, RC outperforms BPTT approaches in terms of predictive performance and in capturing of the long-term statistics, while at the same time requiring much less training time. However, in the case of reduced order data, large scale RC models can be unstable and more likely than the BPTT algorithms to diverge. In contrast, RNNs trained via BPTT show superior forecasting abilities and capture well the dynamics of reduced order systems. Furthermore, the present study quantifies for the first time the Lyapunov Spectrum of the KS equation with BPTT, achieving similar accuracy as RC. This study establishes that RNNs are a potent computational framework for the learning and forecasting of complex spatiotemporal systems. [ABSTRACT FROM AUTHOR]

Despite extensive experimental and computational investigations, the accurate determination of the structural composition of biological tendons remains elusive. Here we infer the structural compositions of tendons by coupling a finite element model with fascicle experimental data through a Bayesian uncertainty quantification framework. We present a mechanical model of the fascicle’s geometric and material properties based on its constituents and employ the Bayesian framework to infer its parameters. The finite element model is optimized for helical geometries to reduce the computational cost associated with the Bayesian inference. We establish a link between the fiber and the fascicle tendon scale and identify an appropriate range of mechanically compatible material and geometric properties to quantify the tendon properties. These findings could serve as a basis for the design of artificial tendons. [ABSTRACT FROM AUTHOR]

We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure. [ABSTRACT FROM AUTHOR]

Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start. [ABSTRACT FROM AUTHOR]

We present Π4U, 1 an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow. [ABSTRACT FROM AUTHOR]

Predictions in the behavior of granular materials using Discrete Element Methods (DEM) hinge on the employed interaction potentials. Here we introduce a data driven, Bayesian framework to quantify DEM predictions. Our approach relies on experimentally measured coefficients of restitution for single steel particle–wall collisions. The calibration data entail both tangential and normal coefficients of restitution, for varying impact angles and speeds of the bouncing particle. The parametric uncertainty in multiple Force–Displacement models is estimated using an enhanced Transitional Markov Chain Monte Carlo implemented efficiently on parallel computer architectures. In turn, the parametric model uncertainties are propagated to predict Quantities of Interest (QoI) for two testbed applications: silo discharge and vibration induced mass-segregation. This work demonstrates that the classical way of calibrating DEM potentials, through parameter optimization, is insufficient and it fails to provide robust predictions. The present Bayesian framework provides robust predictions for the behavior of granular materials using DEM simulations. Most importantly the results demonstrate the importance of including parametric and modeling uncertainties in the potentials employed in Discrete Element Methods. [ABSTRACT FROM AUTHOR]

Abstract: In the last two decades it has been proposed several times that a non-monotonic profile might fit the average lower mantle radial viscosity. Most proposed profiles consist in a more or less broad viscosity hill in the middle of the mantle, at a depth roughly between 1200km and 2000km. Also many tomographic models display strong signals of the presence of “fast” material lying at mid mantle depths and a recent spectral analysis of seismic tomography shows a very clear transition for degree up to around 16 at a less than 1500km depth. Finally latest works, both theoretical and experimental, on the high-to-low-spin transition for periclase, have suggested that the high-spin to low-spin transition of Fe++ might lie at the heart of all these observations. To verify the dynamical compatibility between possible mantle profile and observed tomographic images and compare them with possible mineral physics scenarios, such as the spin transition, we employ here a recently developed Fast Multipole-accelerated Boundary Element Method (FMM-BEM), a numerical approach for solving the viscous momentum equation in a global spherical setting, for simulating the interaction of an individual slab with a mid mantle smooth discontinuity in density and viscosity. We have focused on the complexities induced to the behaviour of average and very large plates O (2000–10,000km), characteristic of the Farallon, Tethys and Pacific plate subducting during the Cenozoic, demonstrating that the a mid mantle density and/or viscosity discontinuity produces a strong alteration of the sinking velocity and an intricate set of slab morphologies. We also employ the Kula–Farallon plate system subducting at 60Ma as a paradigmatic case, which reveals the best high resolution tomography models and clearly suggests an interaction with a strong and/or denser layer in the mantle. Our 38 models show that a plate might or might not penetrate into the lowest mantle and might stall in the mid lower mantle for long periods, depending on the radial profiles of density and viscosity, within a realistic range (viscosity 1, 10 or 100 times more viscous of the rest of the mantle, and a change of differential density in the range −2% to 2%), of a transitional layer of 200km or 500km. We conclude that a layer with high viscosity or negative density would naturally trigger the observed geodynamic snapshot. We finally propose a scenario in which the long time accumulation of depleted slabs in the mid mantle would give rise to a partially chemically stratified mantle, starting from the less prominent high-spin to low-spin contribution on the basis of mantle density and rheology. [Copyright &y& Elsevier]

Abstract: We present a multiscale algorithm that couples coarse grained molecular dynamics (CGMD) with continuum solver. The coupling requires the imposition of non-periodic boundary conditions on the coarse grained Molecular Dynamics which, when not properly enforced, may result in spurious fluctuations of the material properties of the system represented by CGMD. In this paper we extend a control algorithm originally developed for atomistic simulations , to conduct simulations involving coarse grained water molecules without periodic boundary conditions. We demonstrate the applicability of our method in simulating more complex systems by performing a non-periodic Molecular Dynamics simulation of a DPPC lipid in liquid coarse grained water. [Copyright &y& Elsevier]

Abstract: This paper presents a highly efficient parallel particle–mesh (PPM) library, based on a unifying particle formulation for the simulation of continuous systems. In this formulation, the grid-free character of particle methods is relaxed by the introduction of a mesh for the reinitialization of the particles, the computation of the field equations, and the discretization of differential operators. The present utilization of the mesh does not detract from the adaptivity, the efficient handling of complex geometries, the minimal dissipation, and the good stability properties of particle methods. The coexistence of meshes and particles, allows for the development of a consistent and adaptive numerical method, but it presents a set of challenging parallelization issues that have hindered in the past the broader use of particle methods. The present library solves the key parallelization issues involving particle–mesh interpolations and the balancing of processor particle loading, using a novel adaptive tree for mixed domain decompositions along with a coloring scheme for the particle–mesh interpolation. The high parallel efficiency of the library is demonstrated in a series of benchmark tests on distributed memory and on a shared-memory vector architecture. The modularity of the method is shown by a range of simulations, from compressible vortex rings using a novel formulation of smooth particle hydrodynamics, to simulations of diffusion in real biological cell organelles. The present library enables large scale simulations of diverse physical problems using adaptive particle methods and provides a computational tool that is a viable alternative to mesh-based methods. [Copyright &y& Elsevier]

Abstract: We study the wetting of doped single- and multi-walled carbon nanotubes by water droplets using molecular dynamics simulations. Chemisorbed hydrogen is considered as a model of surface impurities. We study systems with varying densities of surface impurities and we observe increased wetting, as compared to the pristine nanotube case, attributed to the surface dipole moment that changes the orientation of the interfacial water. We demonstrate that the nature of the impurity is important as here hydrogen induces the formation of an extended hydrogen bond network between the water molecules and the doping sites leading to enhanced wetting. [Copyright &y& Elsevier]

We perform molecular dynamics (MD) simulations to study the hydrophobic–hydrophilic behavior of pairs of C60 fullerene molecules and single wall carbon nanotubes in water. The interaction potentials involve a fully atomistic description of the fullerenes or carbon nanotubes and the water is modeled using the flexible SPC model. Both unconstrained and constrained MD simulations are carried out. We find that these systems display drying, as evidenced by expulsion of the interstitial water, when the C60 and carbon nanotubes are separated by less than 12, and 9–10 A˚, respectively. From the constrained simulations, the computed mean force between two carbon nanotubes in water exhibits a maximum at a tube spacing of 5.0 A˚ which corresponds to approximately one unstable layer of interstitial water molecules. The main contribution to the force stems from the van der Waals attraction between the carbon surfaces. The minimum in the potential of mean force has a value of −17 kJ mol−1 A˚−1 at a tube spacing of 3.5 A˚. [Copyright &y& Elsevier]