相关论文: Rare Event Sampling Improves Mercury Instability S…
The long-term stability of the Solar System is an issue of significant scientific and philosophical interest. The mechanism leading to instability is Mercury's eccentricity being pumped up so high that Mercury either collides with Venus or…
Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here we present a new…
Due to the chaotic nature of the Solar System, the question of its dynamic long-term stability can only be answered in a statistical sense, e.g. based on numerical ensemble integrations of nearby orbits. Destabilization, including…
Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…
Mercury's orbit can destabilize, generally resulting in a collision with either Venus or the Sun. Chaotic evolution can cause g1 to decrease to the approximately constant value of g5 and create a resonance. Previous work has approximated…
We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space $\mathbb R^d$ and discrete time steps (i.e. a discrete-time $\mathbb…
We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm.…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…
Numerical integrations of the Solar System have been carried out for decades. Their results have been used, for example, to determine whether the Solar System is chaotic, whether Mercury's orbit is stable, or to help discern Earth's climate…
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic…
Bayesian inversions followed by estimations of rare event probabilities are often needed to analyse groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution…
Due to the chaotic nature of the Solar System, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
Of the solar system's four terrestrial planets, the origin of Mercury is perhaps the most mysterious. Modern numerical simulations designed to model the dynamics of terrestrial planet formation systematically fail to replicate Mercury;…
Extreme weather events epitomize high cost: to society through their physical impacts, and to computer servers that simulate them to assess risk and advance physical understanding. It costs hundreds of simulation years to sample a few…
Multilevel Splitting methods, also called Sequential Monte-Carlo or \emph{Subset Simulation}, are widely used methods for estimating extreme probabilities of the form $P[S(\mathbf{U}) > q]$ where $S$ is a deterministic real-valued function…
Many quantum technologies rely on high-precision dynamics, which raises the question of how these are influenced by the experimental uncertainties that are always present in real-life settings. A standard approach in the literature to…
We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte…