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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.

Experience replay (ER) is a fundamental component of off-policy deep reinforcement learning (RL). ER recalls experiences from past iterations to compute gradient estimates for the current policy, increasing data-efficiency. However, the accuracy of such updates may deteriorate when the policy diverges from past behaviors and can undermine the performance of ER. Many algorithms mitigate this issue by tuning hyper-parameters to slow down policy changes. An alternative is to actively enforce the similarity between policy and the experiences in the replay memory. We introduce Remember and Forget Experience Replay (ReF-ER), a novel method that can enhance RL algorithms with parameterized policies. ReF-ER (1) skips gradients computed from experiences that are too unlikely with the current policy and (2) regulates policy changes within a trust region of the replayed behaviors. We couple ReF-ER with Q-learning, deterministic policy gradient and off-policy gradient methods. We find that ReF-ER consistently improves the performance of continuous-action, off-policy RL on fully observable benchmarks and partially observable flow control problems.

Controlled gliding is one of the most energetically efficient modes of transportation for natural and human powered fliers. Here we demonstrate that gliding and landing strategies with different optimality criteria can be identified through deep reinforcement learning without explicit knowledge of the underlying physics. We combine a two dimensional model of a controlled elliptical body with deep reinforcement learning (D-RL) to achieve gliding with either minimum energy expenditure, or fastest time of arrival, at a predetermined location. In both cases the gliding trajectories are smooth, although energy/time optimal strategies are distinguished by small/high frequency actuations. We examine the effects of the ellipse's shape and weight on the optimal policies for controlled gliding. Surprisingly, we find that the model-free reinforcement learning leads to more robust gliding than model-based optimal control strategies with a modest additional computational cost. We also demonstrate that the gliders with D-RL can generalize their strategies to reach the target location from previously unseen starting positions. The model-free character and robustness of D-RL suggests a promising framework for developing mechanical devices capable of exploiting complex flow environments.

Glioblastoma is a highly invasive brain tumor, whose cells infiltrate surrounding normal brain tissue beyond the lesion outlines visible in the current medical scans. These infiltrative cells are treated mainly by radiotherapy. Existing radiotherapy plans for brain tumors derive from population studies and scarcely account for patient-specific conditions. Here we provide a Bayesian machine learning framework for the rational design of improved, personalized radiotherapy plans using mathematical modeling and patient multimodal medical scans. Our method, for the first time, integrates complementary information from high resolution MRI scans and highly specific FET-PET metabolic maps to infer tumor cell density in glioblastoma patients. The Bayesian framework quantifies imaging and modeling uncertainties and predicts patient-specific tumor cell density with confidence intervals. The proposed methodology relies only on data acquired at a single time point and thus is applicable to standard clinical settings. An initial clinical population study shows that the radiotherapy plans generated from the inferred tumor cell infiltration maps spare more healthy tissue thereby reducing radiation toxicity while yielding comparable accuracy with standard radiotherapy protocols. Moreover, the inferred regions of high tumor cell densities coincide with the tumor radioresistant areas, providing guidance for personalized dose-escalation. The proposed integration of multimodal scans and mathematical modeling provides a robust, non-invasive tool to assist personalized radiotherapy design., Comment: Copyright (c) 2019 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. Accepted to IEEE Transactions on Medical Imaging

We investigate the process of cloud cavitation collapse through large-scale simulation of a cloud composed of 12500 gas bubbles. A finite volume scheme is used on a structured Cartesian grid to solve the Euler equations, and the bubbles are discretized by a diffuse interface method. We investigate the propagation of the collapse wave front through the cloud and provide comparisons to simplified models. We analyze the flow field to identify each bubble of the cloud and its associated microjet. We find that the oscillation frequency of the bubbles and the velocity magnitude of the microjets depend on the local strength of the collapse wave and hence on the radial position of the bubbles in the cloud. At the same time, the direction of the microjets is influenced by the distribution of the bubbles in its vicinity. Finally, an analysis of the pressure pulse spectrum shows that the pressure pulse rate is well captured by an exponential law., Comment: 24 pages, 22 figures

Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection of the governing equations have limited applicability due to the large intrinsic dimensionality of the underlying attractor but also the complexity of the transient events. An alternative approach is data-driven techniques that aim to quantify the dynamics of specific modes utilizing data-streams. Several of these approaches have improved performance by expanding the state representation using delayed coordinates. However, such strategies are limited in regions of the phase space where there is a small amount of data available, as is the case for extreme events. In this work, we develop a blended framework that integrates an imperfect model, obtained from projecting equations into a subspace that still contains crucial dynamical information, with data-streams through a recurrent neural network (RNN) architecture. In particular, we employ the long-short-term memory (LSTM), to model portions of the dynamics which cannot be accounted by the equations. The RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected in the reduced-order space. In this way, the data-driven model improves the imperfect model in regions where data is available, while for locations where data is sparse the imperfect model still provides a baseline for the prediction of the system dynamics. We assess the developed framework on two challenging prototype systems exhibiting extreme events and show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. The improvement is more significant in regions associated with extreme events, where data is sparse., Comment: Submitted to PLOS ONE on March 8, 2018

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks., Comment: 31 pages

Fish in schooling formations navigate complex flow-fields replete with mechanical energy in the vortex wakes of their companions. Their schooling behaviour has been associated with evolutionary advantages including collective energy savings. How fish harvest energy from their complex fluid environment and the underlying physical mechanisms governing energy-extraction during collective swimming, is still unknown. Here we show that fish can improve their sustained propulsive efficiency by actively following, and judiciously intercepting, vortices in the wake of other swimmers. This swimming strategy leads to collective energy-savings and is revealed through the first ever combination of deep reinforcement learning with high-fidelity flow simulations. We find that a `smart-swimmer' can adapt its position and body deformation to synchronise with the momentum of the oncoming vortices, improving its average swimming-efficiency at no cost to the leader. The results show that fish may harvest energy deposited in vortices produced by their peers, and support the conjecture that swimming in formation is energetically advantageous. Moreover, this study demonstrates that deep reinforcement learning can produce navigation algorithms for complex flow-fields, with promising implications for energy savings in autonomous robotic swarms., Comment: 26 pages, 14 figures

We propose the $S$-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the $\tau$-leaping and $R$-leaping algorithms. These algorithms are known to be efficient under different conditions; the $\tau$-leaping is efficient for non-stiff systems or systems with partial equilibrium, while the $R$-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the $\tau$-leaping with the effective sampling procedure from the $R$-leaping algorithm. The $S$-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the $S$-leaping outperforms both methods. We demonstrate the performance and the accuracy of the $S$-leaping in comparison with the $\tau$-leaping and $R$-leaping on a number of benchmark systems involving biological reaction networks.

Video prediction models based on convolutional networks, recurrent networks, and their combinations often result in blurry predictions. We identify an important contributing factor for imprecise predictions that has not been studied adequately in the literature: blind spots, i.e., lack of access to all relevant past information for accurately predicting the future. To address this issue, we introduce a fully context-aware architecture that captures the entire available past context for each pixel using Parallel Multi-Dimensional LSTM units and aggregates it using blending units. Our model outperforms a strong baseline network of 20 recurrent convolutional layers and yields state-of-the-art performance for next step prediction on three challenging real-world video datasets: Human 3.6M, Caltech Pedestrian, and UCF-101. Moreover, it does so with fewer parameters than several recently proposed models, and does not rely on deep convolutional networks, multi-scale architectures, separation of background and foreground modeling, motion flow learning, or adversarial training. These results highlight that full awareness of past context is of crucial importance for video prediction., Comment: 19 pages. ECCV 2018 oral presentation. Project webpage is at https://wonmin-byeon.github.io/publication/2018-eccv

Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model parameters for a disease spreading on a network of communities from limited, noisy observations; the state-of-the-art computational framework compensates for the model complexity by exploiting massively parallel computing architectures. Using noisy, synthetic data, we show the potential of the approach to perform robust model fitting and additionally demonstrate that we can effectively identify the disease origin via Bayesian model selection. As disease-related data are increasingly available, the proposed framework has broad practical relevance for the prediction and management of epidemics.

The Lennard-Jones (LJ) potential is a cornerstone of Molecular Dynamics (MD) simulations and among the most widely used computational kernels in science. The potential models atomistic attraction and repulsion with century old prescribed parameters ($q=6, \; p=12$, respectively), originally related by a factor of two for simplicity of calculations. We re-examine the value of the repulsion exponent through data driven uncertainty quantification. We perform Hierarchical Bayesian inference on MD simulations of argon using experimental data of the radial distribution function (RDF) for a range of thermodynamic conditions, as well as dimer interaction energies from quantum mechanics simulations. The experimental data suggest a repulsion exponent ($p \approx 6.5$), in contrast to the quantum simulations data that support values closer to the original ($p=12$) exponent. Most notably, we find that predictions of RDF, diffusion coefficient and density of argon are more accurate and robust in producing the correct argon phase around its triple point, when using the values inferred from experimental data over those from quantum mechanics simulations. The present results suggest the need for data driven recalibration of the LJ potential across MD simulations.

We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties related to their initial spatial arrangement. The resulting 2000-dimensional space is sampled using a non-intrusive and computationally efficient Multi-Level Monte Carlo (MLMC) methodology. We introduce novel optimal control variate coefficients to enhance the variance reduction in MLMC. The proposed optimal fidelity MLMC leads to more than two orders of magnitude speedup when compared to standard Monte Carlo methods. We identify large uncertainties in the location and magnitude of the peak pressure pulse and present its statistical correlations and joint probability density functions with the geometrical characteristics of the cloud. Characteristic properties of spatial cloud structure are identified as potential causes of significant uncertainties in exerted collapse pressures.

We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of polynomial functions, we show that the HSM is capable of separating different types of uncertainties in a system and quantifying uncertainty of reduced order models under the Bayesian model class selection framework. To tackle the huge computational cost for analyzing HSM, we propose an efficient approximation scheme based on Importance Sampling and Empirical Interpolation Method. We illustrate our method using two examples - a Molecular Dynamics simulation for Krypton and a pharmacokinetic/pharmacodynamic model for cancer drug.

We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin transition kernels with the advantages of global exploration by a population based sampling algorithm, the Transitional Markov Chain Monte Carlo (TMCMC). The Langevin diffusion process is determined by either the Hessian or the Fisher Information of the target distribution with appropriate modifications for non positive definiteness. The present methods is shown to be superior over other population based algorithms, in sampling probability distributions for which gradients are available and is shown to handle otherwise unidentifiable models. We demonstrate the capabilities and advantages of the method in computing the posterior distribution of the parameters in a Pharmacodynamics model, for glioma growth and its drug induced inhibition, using clinical data.

The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self-propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers, and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body-fitted grids are used. Alternatively, such simulations may employ penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow- induced forces on the surface of both rigid and deforming bodies, in simulations using re-meshed vortex methods and Brinkman penalization. The pressure field is recovered from the velocity by solving a Poisson's equation using the Green's function approach, augmented with a fast multipole expansion and a tree- code algorithm. The viscous forces are determined by evaluating the strain-rate tensor on the surface of deforming bodies, and on a 'lifted' surface in simulations involving rigid objects. We present results for benchmark flows demonstrating that we can obtain an accurate distribution of flow-induced surface-forces. The capabilities of our method are demonstrated using simulations of self-propelled swimmers, where we obtain the pressure and shear distribution on their deforming surfaces.

We study the fluid dynamics of two fish-like bodies with synchronised swimming patterns. Our studies are based on two-dimensional simulations of viscous incompressible flows. We distinguish between motion patterns that are externally imposed on the swimmers and self-propelled swimmers that learn manoeuvres to achieve certain goals. Simulations of two rigid bodies executing pre-specified motion indicate that flow-mediated interactions can lead to substantial drag reduction and may even generate thrust intermittently. In turn we examine two self-propelled swimmers arranged in a leader-follower configuration, with a-priori specified body-deformations. We find that the swimming of the leader remains largely unaffected, while the follower experiences either an increase or decrease in swimming speed, depending on the initial conditions. Finally, we consider a follower that synchronises its motion so as to minimise its lateral deviations from the leader's path. The leader employs a steady gait while the follower uses a reinforcement learning algorithm to adapt its swimming-kinematics. We find that swimming in a synchronised tandem can yield up to about 30% reduction in energy expenditure for the follower, in addition to a 20% increase in its swimming-efficiency. The present results indicate that synchronised swimming of two fish can be energetically beneficial.

Schooling, an archetype of collective behavior, emerges from the interactions of fish responding to visual and other informative cues mediated by their aqueous environment. In this context, a fundamental and largely unexplored question concerns the role of hydrodynamics. Here, we investigate schooling by modeling swimmers as vortex dipoles whose interactions are governed by the Biot-Savart law. When we enhance these dipoles with behavioral rules from classical agent based models we find that they do not lead robustly to schooling due to flow mediated interactions. In turn, we present dipole swimmers equipped with adaptive decision-making that learn, through a reinforcement learning algorithm, to adjust their gaits in response to non-linearly varying hydrodynamic loads. The dipoles maintain their relative position within a formation by adapting their strength and school in a variety of prescribed geometrical arrangements. Furthermore, we identify schooling patterns that minimize the individual and the collective swimming effort, through an evolutionary optimization. The present work suggests that the adaptive response of individual swimmers to flow-mediated interactions is critical in fish schooling., Comment: 18 pages, 12 figures

Rough surfaces immersed under water remain practically dry if the liquid-solid contact is on roughness peaks, while the roughness valleys are filled with gas. Mechanisms that prevent water from invading the valleys are well studied. However, to remain practically dry under water, additional mechanisms need consideration. This is because trapped gas (e.g. air) in the roughness valleys can dissolve into the water pool, leading to invasion. Additionally, water vapor can also occupy the roughness valleys of immersed surfaces. If water vapor condenses, that too leads to invasion. These effects have not been investigated, and are critically important to maintain surfaces dry under water. In this work, we identify the critical roughness scale below which it is possible to sustain the vapor phase of water and/or trapped gases in roughness valleys - thus keeping the immersed surface dry. Theoretical predictions are consistent with molecular dynamics simulations and experiments., Comment: Manuscript: 19 pages, 4 figures, 1 table. Supplementary Information: 20 pages; 10 figures, 2 tables

The Living Earth Simulator (LES) is one of the core components of the FuturICT architecture. It will work as a federation of methods, tools, techniques and facilities supporting all of the FuturICT simulation-related activities to allow and encourage interactive exploration and understanding of societal issues. Society-relevant problems will be targeted by leaning on approaches based on complex systems theories and data science in tight interaction with the other components of FuturICT. The LES will evaluate and provide answers to real-world questions by taking into account multiple scenarios. It will build on present approaches such as agent-based simulation and modeling, multiscale modelling, statistical inference, and data mining, moving beyond disciplinary borders to achieve a new perspective on complex social systems.

We present a simulation for the interactions of shockwaves with light spherical density inhomogeneities. Euler equations for two-phase compressible flows are solved in a 3D uniform resolution finite volume based solver using 5th order WENO reconstructions of the primitive quantities, HLL-type numerical fluxes and 3rd order TVD time stepping scheme. In this study, a normal Mach 3 shockwave in air is directed at a helium bubble with an interface Atwood number of -0.76. We employ 4 billion cells on a supercomputing cluster and demonstrate the development of this flow until relatively late times. Shock passage compresses the bubble and deposits baroclinic vorticity on the interface. Initial distribution of the vorticity and compressions lead to the formation of an air jet, interface roll-ups and the formation of a long lasting vortical core, the white core. Compressed upstream of the bubble turns into a mixing zone and as the vortex ring distances from this mixing zone, a plume-shaped region is formed and sustained. Close observations have been reported in previous experimental works. The visualization is presented in a fluid dynamics video., Comment: 1 page PDF file containing the abstract, references and one image, 2 movies, 1 low quality (<10MB) and 1 HD quality (<150MB) for APS DFD 2012

We present simulations of the vortex dynamics associated with the self-propelled motion of jellyfish. The geometry is obtained from image segmentation of video recordings from live jellyfish. The numerical simulations are performed using three-dimensional viscous, vortex particle methods with Brinkman penalization to impose the kinematics of the jellyfish motion. We study two types of strokes recorded in the experiment1. The first type (stroke A) produces two vortex rings during the stroke: one outside the bell during the power stroke and one inside the bell during the recovery stroke. The second type (stroke B) produces three vortex rings: one ring during the power stroke and two vortex rings during the recovery stroke. Both strokes propel the jellyfish, with stroke B producing the highest velocity. The speed of the jellyfish scales with the square root of the Reynolds number. The simulations are visualized in a fluid dynamics video., Comment: 1 page, 1 figure

We propose a hybrid model, coupling Lattice Boltzmann and Molecular Dynamics models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach., Comment: 14 pages, 5 figures