Related papers: Enabling High-Dimensional Hierarchical Uncertainty…

We introduce Universal Solution Manifold Network (USM-Net), a novel surrogate model, based on Artificial Neural Networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. Our…

Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the past two decades, a growing interest has been devoted to stochastic finite element method (SFEM) for the propagation of…

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains…

We propose Efficient Neural Architecture Search (ENAS), a fast and inexpensive approach for automatic model design. In ENAS, a controller learns to discover neural network architectures by searching for an optimal subgraph within a large…

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…

The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…

Monte Carlo simulation is often used for the reliability assessment of power systems, but it converges slowly when the system is complex. Multilevel Monte Carlo (MLMC) can be applied to speed up computation without compromises on model…

Quantum circuit simulation provides the foundation for the development of quantum algorithms and the verification of quantum supremacy. Among the various methods for quantum circuit simulation, tensor network contraction has been increasing…

Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…

Producing large complex simulation datasets can often be a time and resource consuming task. Especially when these experiments are very expensive, it is becoming more reasonable to generate synthetic data for downstream tasks. Recently,…

Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…

We propose, and illustrate via a neural network example, two different approaches to coarse-graining large heterogeneous networks. Both approaches are inspired from, and use tools developed in, methods for uncertainty quantification in…

Using Artificial Neural Networks (ANN) for nonlinear system identification has proven to be a promising approach, but despite of all recent research efforts, many practical and theoretical problems still remain open. Specifically, noise…

Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires…

Semantic segmentation of microscopy images is a critical task for high-throughput materials characterisation, yet its automation is severely constrained by the prohibitive cost, subjectivity, and scarcity of expert-annotated data. While…

Predicting the behavior of complex systems in engineering often involves significant uncertainty about operating conditions, such as external loads, environmental effects, and manufacturing variability. As a result, uncertainty…

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…

The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop…

This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…

Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a…