Significance Quantifying the departure from Gaussianity of wave-height distribution in seas and thereby estimating likelihood appearance rogue waves is a long-standing problem with important practical implications for boats naval structures. Here, procedure introduced to identify ocean states that are precursors waves, which could permit their early detection. Our findings indicate obey large deviation principle—i.e., they dominated by single realizations—which our method calculates solving...

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one the last open problems classical physics. In this review we discuss recent developments related to application instanton methods turbulence. Instantons are saddle point configurations underlying path integrals. They equivalent minimizers Freidlin–Wentzell action and known be able characterize rare events such systems. While there an impressive body work concerning their analytical...

A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random with different degrees nonlinearity are mechanically generated free to propagate along the flume. Strong evidence given that observed hydrodynamic instantons, is, saddle point configurations action associated stochastic model wave system. As shown here, these instantons complex spatiotemporal field which can be defined using mathematical framework large deviation...

We apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity model and analyse their interplay. First, drawing from the theory of quasi-potentials, viewing state space as energy landscape with valleys mountain ridges, we infer relative likelihood identified multistable investigate most likely transition trajectories well expected times between them. Second, harnessing techniques science, specifically manifold learning, characterize...

Abstract Sharp large deviation estimates for stochastic differential equations with small noise, based on minimizing the Freidlin–Wentzell action functional under appropriate boundary conditions, can be obtained by integrating certain matrix Riccati along minimizers or instantons, either forward backward in time. Previous works this direction often rely existence of isolated positive definite second variation. By adopting techniques from field theory and explicitly evaluating prefactors as...

An overview of rare event algorithms based on large deviation theory (LDT) is presented. It covers a range numerical schemes to compute the minimizer in various setups and discusses best practices, common pitfalls, implementation tradeoffs. Generalizations, extensions, improvements minimum action methods are proposed. These tested example problems which illustrate several difficulties arise, e.g., when forcing degenerate or multiplicative, systems infinite-dimensional. Generalizations...

There is a reasonable possibility that the present-day Atlantic Meridional Overturning Circulation in bistable regime, hence it relevant to compute pathways of noise-induced transitions between stable equilibrium states. Here, most probable transition pathway tipping northern overturning circulation spatially-continuous two-dimensional model with surface temperature and stochastic salinity forcings computed directly using large deviation theory. This reveals fluid dynamical mechanisms such...

We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the shows both static and a limit cycle, in which rising global causes dense bacterial colony form, then declines by local cell death, before dispersing reinitiate cycle. Adding fluctuations, we find that colonies are now metastable, moving between spatial locations via rare strongly nonequilibrium pathways, whereas cycle becomes almost periodic such after...

A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on predictions we make from them. This question naturally lends itself a probabilistic formulation, by making unknown model parameters random with given statistics. Here this approach used concert tools large deviation theory (LDT) and optimal control estimate probability some observables dynamical system go above threshold after time, prior statistical information...

We investigate the spatio-temporal structure of most likely configurations realizing extremely high vorticity or strain in stochastically forced three-dimensional incompressible Navier-Stokes equations. Most are computed by numerically finding highest probability velocity field an extreme constraint as solution a large optimization problem. High-vorticity identified pinched vortex filaments with swirl, while high-strain correspond to counter-rotating rings. additionally observe that for and...

The rupture of thin liquid films on solid surfaces is conventionally assumed to be driven by intermolecular forces, in the so-called spinodal regime. Here, a theoretical framework created for experimentally observed thermal regime, which fluctuation-induced nanowaves films. Fluctuating hydrodynamics able capture this regime and its predictions are verified molecular simulations. Rare-event theory then applied field first time reveal novel picture how when rogue create rupture.

Abstract Freidlin‐Wentzell theory of large deviations can be used to compute the likelihood extreme or rare events in stochastic dynamical systems via solution an optimization problem. The approach gives exponential estimates that often need refined calculation a prefactor. Here it is shown how perform these computations practice. Specifically, sharp asymptotic are derived for expectations, probabilities, and mean first passage times form geared towards numerical purposes: they require...

We address the question whether one can identify instantons in direct numerical simulations of stochastically driven Burgers equation.For this purpose, we first solve instanton equations using Chernykh-Stepanov method [Phys.Rev. E 64, 026306 (2001)].These results are then compared to by introducing a filtering technique extract prescribed rare events from massive data sets realizations.Using approach entire time history evolution which allows us different phases predicted Chernykh and...

Abstract In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential scaling. this paper, we derive a general, closed form expression for leading prefactor contribution fluctuations around trajectory computation probability density functions general observables. The key technique is applying Gel’fand–Yaglom...

Abstract There is strong evidence that the present-day Atlantic Meridional Overturning Circulation (AMOC) in a bi-stable regime and hence it important to determine probabilities pathways for noise-induced transitions between its equilibrium states. Here, using Large Deviation Theory (LDT), most probable transition collapse recovery of AMOC are computed stochastic box model World Ocean. This allows us physical mechanisms transitions. We show likely path an starts paradoxically with...

In multistable dynamical systems driven by weak Gaussian noise, transitions between competing states are often assumed to pass via a saddle on the separating basin boundary. By contrast, we show that timescale separation can cause avoidance in nongradient systems. Using toy models from neuroscience and ecology, study cases where sample deviate strongly instanton predicted Freidlin-Wentzell theory, even for finite noise. We attribute this flat quasipotential present an approach based...

A method is presented to compute minimizers (instantons) of action functionals using arclength parametrization Hamilton's equations. This can be interpreted as a local variant the geometric minimum introduced Freidlin--Wentzell functional that arises in context large deviation theory for stochastic differential The particularly well suited calculate expectations dominated by noise-induced excursions from deterministically stable fixpoints. Its simplicity and computational efficiency are...

Instanton calculations are performed in the context of stationary Burgers turbulence to estimate tails probability density function (PDF) velocity gradients.These results then compared those obtained from massive direct numerical simulations (DNS) randomly forced equation.The instanton predictions shown agree with DNS a wide range regimes, including that far limiting cases previously considered literature.These settle controversy relevance approach for prediction gradient PDF tail...

Abstract Large deviation theory and instanton calculus for stochastic systems are widely used to gain insight into the evolution probability of rare events. At its core lies fact that events are, under right circumstances, dominated by their least unlikely realization. Their computation through a saddle-point approximation path integral corresponding field then reduces an inefficient sampling problem deterministic optimization problem: finding smallest action, instanton. In presence heavy...

Abstract We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their efficiency does not degrade upon temporal possibly spatial refinement. For purpose, extend algorithms based the Laplace method estimating of an to infinite dimensional path space. The limiting exponential scaling using a single realization random...

Abstract Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers suitable action functional. Due to high number degrees freedom multi-dimensional flows, traditional global minimization techniques quickly become prohibitive memory requirements. We outline novel method for finding minimizing trajectory wide class problems that typically...

Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed situations where the scale separation gives rise to a slow manifold with bifurcation. This analysis is performed within realm of large deviation theory. It shown that these non-equilibrium make use reaction channel created by bifurcation structure manifold, leading vastly increased transition rates. Several examples used illustrate findings, including an insect outbreak model,...