Related papers: Estimating Failure Probability with Neural Operato…

Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…

We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo. We derive the optimal number of nested simulations and prove that the algorithm is…

We address the problem of maintaining high voltage power transmission networks in security at all time, namely anticipating exceeding of thermal limit for eventual single line disconnection (whatever its cause may be) by running slow, but…

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…

Due to the unprecedented success of deep learning, it has become an integral component in several multimedia computing applications in todays world. Unfortunately, deep learning systems are not perfect and can fail, sometimes abruptly,…

We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…

We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…

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…

Transmission expansion planning (TEP) plays a critical role in ensuring power system reliability and facilitating the integration of renewable energy resources. However, this process requires planners to constantly deal with significant…

The hybridizations of machine learning and quantum physics have caused essential impacts to the methodology in both fields. Inspired by quantum potential neural network, we here propose to solve the potential in the Schrodinger equation…

The problem considered in this paper is the online diagnosis of Automated Production Systems with sensors and actuators delivering discrete binary signals that can be modeled as Discrete Event Systems. Even though there are numerous…

In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…

In this paper we analyze the use of subjective logic as a framework for performing approximate transformations over probability distribution functions. As for any approximation, we evaluate subjective logic in terms of computational…

Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…

We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by…

Assessing reliably the confidence of a deep neural network and predicting its failures is of primary importance for the practical deployment of these models. In this paper, we propose a new target criterion for model confidence,…

A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions…

Existing variance reduction techniques used in stochastic simulations for rare event analysis still require a substantial number of model evaluations to estimate small failure probabilities. In the context of complex, nonlinear finite…

Learning-based methodologies increasingly find applications in safety-critical domains like autonomous driving and medical robotics. Due to the rare nature of dangerous events, real-world testing is prohibitively expensive and unscalable.…

We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…