Related papers: Subset Simulation Method for Rare Event Estimation…
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…
This brief introduction to Model Predictive Control specifically addresses stochastic Model Predictive Control, where probabilistic constraints are considered. A simple linear system subject to uncertainty serves as an example. The Matlab…
We consider the problem of estimating a probability of failure $\alpha$, defined as the volume of the excursion set of a function $f:\mathbb{X} \subseteq \mathbb{R}^{d} \to \mathbb{R}$ above a given threshold, under a given probability…
We outline the basic ideas and techniques underpinning the simulation of stochastic differential equations. In particular we focus on strong simulation and its context. We also provide illustratory examples and sample matlab algorithms for…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
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…
In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the…
The bifurcation method is a way to do rare event sampling -- to estimate the probability of events that are too rare to be found by direct simulation. We describe the bifurcation method and use it to estimate the transition rate of a double…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
Estimation and inference in dynamic discrete choice models often relies on approximation to lower the computational burden of dynamic programming. Unfortunately, the use of approximation can impart substantial bias in estimation and results…
Solving decision problems in complex, stochastic environments is often achieved by estimating the expected outcome of decisions via Monte Carlo sampling. However, sampling may overlook rare, but important events, which can severely impact…
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…
The efficiency of atomic simulations of materials and molecules can rapidly deteriorate when large free energy barriers exist between local minima. We propose smooth basin classification, a universal method to define reaction coordinates…
Estimating the probability of failures or accidents with aerospace systems is often necessary when new concepts or designs are introduced, as it is being done for Autonomous Aircraft. If the design is safe, as it is supposed to be, accident…
We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of…
We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with…
We analyze a lightweight simulation-based inference method that infers simulator parameters using only a regression-based projection of the observed data. After fitting a surrogate linear regression once, the procedure simulates small…
Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…
This paper presents a novel method for rare event detection from an image pair with class-imbalanced datasets. A straightforward approach for event detection tasks is to train a detection network from a large-scale dataset in an end-to-end…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…