46 research outputs found
Forward Flux Sampling for rare event simulations
Rare events are ubiquitous in many different fields, yet they are notoriously
difficult to simulate because few, if any, events are observed in a conventiona
l simulation run. Over the past several decades, specialised simulation methods
have been developed to overcome this problem. We review one recently-developed
class of such methods, known as Forward Flux Sampling. Forward Flux Sampling
uses a series of interfaces between the initial and final states to calculate
rate constants and generate transition paths, for rare events in equilibrium or
nonequilibrium systems with stochastic dynamics. This review draws together a
number of recent advances, summarizes several applications of the method and
highlights challenges that remain to be overcome.Comment: minor typos in the manuscript. J.Phys.:Condensed Matter (accepted for
publication
Local and Global Perspectives on Diffusion Maps in the Analysis of Molecular Systems
Diffusion maps approximate the generator of Langevin dynamics from simulation
data. They afford a means of identifying the slowly-evolving principal modes of
high-dimensional molecular systems. When combined with a biasing mechanism,
diffusion maps can accelerate the sampling of the stationary Boltzmann-Gibbs
distribution. In this work, we contrast the local and global perspectives on
diffusion maps, based on whether or not the data distribution has been fully
explored. In the global setting, we use diffusion maps to identify metastable
sets and to approximate the corresponding committor functions of transitions
between them. We also discuss the use of diffusion maps within the metastable
sets, formalising the locality via the concept of the quasi-stationary
distribution and justifying the convergence of diffusion maps within a local
equilibrium. This perspective allows us to propose an enhanced sampling
algorithm. We demonstrate the practical relevance of these approaches both for
simple models and for molecular dynamics problems (alanine dipeptide and
deca-alanine)
Application of adaptive multilevel splitting to high-dimensional dynamical systems
Stochastic nonlinear dynamical systems can undergo rapid transitions relative
to the change in their forcing, for example due to the occurrence of multiple
equilibrium solutions for a specific interval of parameters. In this paper, we
modify one of the methods developed to compute probabilities of such
transitions, Trajectory-Adaptive Multilevel Sampling (TAMS), to be able to
apply it to high-dimensional systems. The key innovation is a projected
time-stepping approach, which leads to a strong reduction in computational
costs, in particular memory usage. The performance of this new implementation
of TAMS is studied through an example of the collapse of the Atlantic Ocean
Circulation
Data-driven methods to estimate the committor function in conceptual ocean models
In recent years, several climate subsystems have been identified that may undergo a relatively rapid transition compared to the changes in their forcing. Such transitions are rare events in general and simulating long-enough trajectories in order to gather sufficient data to determine transition statistics would be too expensive. Conversely, rare-events algorithms like TAMS (Trajectory-Adaptive Multilevel Sampling) encourage the transition while keeping track of the model statistics. However, this algorithm relies on a score function whose choice is crucial to ensure its efficiency. The optimal score function, called committor function, is in practice very difficult to compute. In this paper, we compare different data-based methods (Analogue Markov Chains, Neural Networks, Reservoir Computing, Dynamical Galerkin Approximation) to estimate the committor from trajectory data. We apply these methods on two models of the Atlantic Ocean circulation featuring very different dynamical behavior. We compare these methods in terms of two measures, evaluating how close the estimate is from the true committor, and in terms of the computational time. We find that all methods are able to extract information from the data in order to provide a good estimate of the committor. Analogue Markov Chains provide a very reliable estimate of the true committor in simple models but prove not so robust when applied to systems with a more complex phase space. Neural network methods clearly stand out by their relatively low testing time, and their training time scales more favorably with the complexity of the model than the other methods. In particular, feedforward neural networks consistently achieve the best performance when trained with enough data, making this method promising for committor estimation in sophisticated climate models.</p
Probabilistic forecasts of extreme heatwaves using convolutional neural networks in a regime of lack of data
Understanding extreme events and their probability is key for the study of
climate change impacts, risk assessment, adaptation, and the protection of
living beings. In this work we develop a methodology to build forecasting
models for extreme heatwaves. These models are based on convolutional neural
networks, trained on extremely long 8,000-year climate model outputs. Because
the relation between extreme events is intrinsically probabilistic, we
emphasise probabilistic forecast and validation. We demonstrate that deep
neural networks are suitable for this purpose for long lasting 14-day heatwaves
over France, up to 15 days ahead of time for fast dynamical drivers (500 hPa
geopotential height fields), and also at much longer lead times for slow
physical drivers (soil moisture). The method is easily implemented and
versatile. We find that the deep neural network selects extreme heatwaves
associated with a North-Hemisphere wavenumber-3 pattern. We find that the 2
meter temperature field does not contain any new useful statistical information
for heatwave forecast, when added to the 500 hPa geopotential height and soil
moisture fields. The main scientific message is that training deep neural
networks for predicting extreme heatwaves occurs in a regime of drastic lack of
data. We suggest that this is likely the case for most other applications to
large scale atmosphere and climate phenomena. We discuss perspectives for
dealing with the lack of data regime, for instance rare event simulations, and
how transfer learning may play a role in this latter task.Comment: 33 pages, 12 figure
Transition Path Sampling and Forward Flux Sampling. Applications to Biological Systems.
The last decade has seen a rapid growth in the number of simulation methods and applications dealing with the sampling of transition pathways of rare nanoscale events. Such studies are crucial, for example, for understanding the mechanism and kinetics of conformational transitions and enzymatic events associated with the function of biomolecules. In this review, a broad account of transition path sampling approaches is provided, starting from the general concepts, progressing to the specific principles that underlie some of the most important methods, and eventually singling out the so-called forward flux sampling method for a more detailed description. This is done because forward flux sampling, despite its appealing simplicity and potential efficiency, has thus far received limited attention from practitioners. While path sampling methods have a widespread application to many types of rare transitional events, here only recent applications involving biomolecules are reviewed, including isomerization, protein folding, and enzyme catalysis.This publication is based on work supported in part by Award No. KUS-C1-018-02, made by King Abdullah University of Science and Technology (KAUST). Additional support from the National Science Foundation Award 0553719 is also gratefully acknowledged. The authors are also grateful to J. Hernandez-Ortiz and P. Bolhuis for allowing us to modify their picture files