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The Dune framework: Basic concepts and recent developments
Get PDFThis paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state Bastian etal. (2008a, 2008b). This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut cells, grid modifications such as adaptation and moving domains, high order discretizations and node level performance, non-smooth multigrid methods, and multiscale methods. A brief discussion on current and future development directions of the framework concludes the paper
Nonasymptotic bounds for suboptimal importance sampling
No full textImportance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically possible, in practice only suboptimal proposal distributions are available and it can often be observed numerically that those can reduce statistical performance significantly, leading to large relative errors and therefore counteracting the original intention. In this article, we provide nonasymptotic lower and upper bounds on the relative error in importance sampling that depend on the deviation of the actual proposal from optimality, and we thus identify potential robustness issues that importance sampling may have, especially in high dimensions. We focus on path sampling problems for diffusion processes, for which generating good proposals comes with additional technical challenges, and we provide numerous numerical examples that support our findings
Machine learning implicit solvation for molecular dynamics.
No full textABSTRACT
Accurate modeling of the solvent environment for biological molecules is crucial for computational biology and drug design. A popular
approach to achieve long simulation time scales for large system sizes is to incorporate the effect of the solvent in a mean-field fashion with
implicit solvent models. However, a challenge with existing implicit solvent models is that they often lack accuracy or certain physical prop-
erties compared to explicit solvent models as the many-body effects of the neglected solvent molecules are difficult to model as a mean field.
Here, we leverage machine learning (ML) and multi-scale coarse graining (CG) in order to learn implicit solvent models that can approximate
the energetic and thermodynamic properties of a given explicit solvent model with arbitrary accuracy, given enough training data. Following
the previous ML–CG models CGnet and CGSchnet, we introduce ISSNet, a graph neural network, to model the implicit solvent potential of
mean force. ISSNet can learn from explicit solvent simulation data and be readily applied to molecular dynamics simulations. We compare the
solute conformational distributions under different solvation treatments for two peptide systems. The results indicate that ISSNet models can
outperform widely used generalized Born and surface area models in reproducing the thermodynamics of small protein systems with respect
to explicit solvent. The success of this novel method demonstrates the potential benefit of applying machine learning methods in accurate
modeling of solvent effects for in silico research and biomedical applications
Deeptime: a Python library for machine learning dynamical models from time series data
No full textAbstract
Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software. Deeptime can be found under https://deeptime-ml.github.io/
Effect of the Hydration Shell on the Carbonyl Vibration in the Ala-Leu-Ala-Leu Peptide
No full textAbstract
The vibrational spectrum of the Ala-Leu-Ala-Leu peptide in solution, computed from first-principles simulations, shows a prominent band in the amide I region that is assigned to stretching of carbonyl groups. Close inspection reveals combined but slightly different contributions by the three carbonyl groups of the peptide. The shift in their exact vibrational signature is in agreement with the different probabilities of these groups to form hydrogen bonds with the solvent. The central carbonyl group has a hydrogen bond probability intermediate to the other two groups due to interchanges between different hydrogen-bonded states. Analysis of the interaction energies of individual water molecules with that group shows that shifts in its frequency are directly related to the interactions with the water molecules in the first hydration shell. The interaction strength is well correlated with the hydrogen bond distance and hydrogen bond angle, though there is no perfect match, allowing geometrical criteria for hydrogen bonds to be used as long as the sampling is sufficient to consider averages. The hydrogen bond state of a carbonyl group can therefore serve as an indicator of the solvent’s effect on the vibrational frequency
Variational approach to fluid-structure interaction via GENERIC
No full textWe present a framework to systematically derive variational formulations for fluid-structure
interaction problems based on thermodynamical driving functionals and geometric structures in
different coordinate systems by suitable transformations within this formulation. Our approach
provides a promising basis to construct structure-preserving discretization strategies
Estimating computational limits on theoretical descriptions of biological cells
No full textThere has been much success recently in theoretically simulating parts of complex biological systems on the molecular level, with the goal of first-principles modeling of whole cells. However, there is the question of whether such simulations can be performed because of the enormous complexity of cells. We establish approximate equations to estimate computation times required to simulate highly simplified models of cells by either molecular dynamics calculations or by solving molecular kinetic equations. Our equations place limits on the complexity of cells that can be theoretically understood with these two methods and provide a first step in developing what can be considered biological uncertainty relations for molecular models of cells. While a molecular kinetics description of the genetically simplest bacterial cell may indeed soon be possible, neither theoretical description for a multicellular system, such as the human brain, will be possible for many decades and may never be possible even with quantum computing
The Design Principles of Discrete Turing Patterning Systems
No full textThe formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in our discrete modelling framework in comparison to the continuous case, in the sense that the presence of an instability does not guarantee a pattern emerging in simulations. We show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought
Lagrangian hairpins in atmospheric boundary layers
No full textIn this poster, we have shown beautiful direct volume renders of finite-time Lyapunov exponent (FTLE) fields applied to a highly stratified Ekman flow. This flow describes the atmospheric boundary layer (ABL) over a smooth flat plate driven by a uniform pressure gradient and experiencing steady rotation in the wall-normal direction.
An interesting result can be observed here. We note that hairpins extracted from different regions in the flow field are oriented in a similar direction i.e., the head of the hairpins point to a similar direction. These results are in-line with our previous observation with the Eulerian Q-criterion [1, 2].
For further details on FTLE, please refer to the work of [3, 4]. FTLE is sometimes referred in literature as direct Lyapunov exponent (DLE).
The Reynolds number is described in terms of the geostrophic wind velocity (G), the laminar Ekman-layer depth (D) and the kinematic viscosity (ν) as Re = GD/ν