Related papers: Noise-robust multi-fidelity surrogate modelling fo…

Variational quantum circuits (VQCs) solving partial differential equations (PDEs) on near-term quantum hardware face a critical challenge: hardware noise degrades solution fidelity and disrupts convergence. We present a systematic study of…

Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not…

We consider a quasilinear parabolic stochastic partial differential equation driven by a multiplicative noise and study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine…

Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…

We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…

Multi-fidelity modeling and learning are important in physical simulation-related applications. It can leverage both low-fidelity and high-fidelity examples for training so as to reduce the cost of data generation while still achieving good…

We introduce CODES, a benchmark for comprehensive evaluation of surrogate architectures for coupled ODE systems. Besides standard metrics like mean squared error (MSE) and inference time, CODES provides insights into surrogate behaviour…

We show that non-exponential fidelity decays in randomized benchmarking experiments on quantum dot qubits are consistent with numerical simulations that incorporate low-frequency noise. By expanding standard randomized benchmarking analysis…

To date, the analysis of high-dimensional, computationally expensive engineering models remains a difficult challenge in risk and reliability engineering. We use a combination of dimensionality reduction and surrogate modelling termed…

Multifidelity surrogate modelling combines data of varying accuracy and cost from different sources. It strategically uses low-fidelity models for rapid evaluations, saving computational resources, and high-fidelity models for detailed…

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been…

This paper considers the surrogate modeling of a complex numerical code in a multifidelity framework when the code output is a time series. Using an experimental design of the low-and high-fidelity code levels, an original Gaussian process…

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and…

This article builds on the recently proposed RB-ML-ROM approach for parameterized parabolic PDEs and proposes a novel hierarchical Trust Region algorithm for solving parabolic PDE constrained optimization problems. Instead of using a…

We consider the numerical approximation of a general second order semi--linear parabolic stochastic partial differential equation (SPDEs) driven by space-time noise, for multiplicative and additive noise. We examine convergence of…

Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle…

Surrogate modeling for complex physical systems typically faces a trade-off between data-fitting accuracy and physical consistency. Physics-consistent approaches typically treat physical laws as soft constraints within the loss function, a…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

This paper presents a comparison of two multi-fidelity methods for the forward uncertainty quantification of a naval engineering problem. Specifically, we consider the problem of quantifying the uncertainty of the hydrodynamic resistance of…