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

Aerodynamic shape optimization in industry still faces challenges related to robustness and scalability. This aspect becomes crucial for advanced optimizations that rely on expensive high-fidelity flow solvers, where computational budget…

Emulating the mapping between quantities of interest and their control parameters using surrogate models finds widespread application in engineering design, including in numerical optimization and uncertainty quantification. Gaussian…

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

Surrogate models for partial-differential equations are widely used in the design of meta-materials to rapidly evaluate the behavior of composable components. However, the training cost of accurate surrogates by machine learning can rapidly…

Computational modeling of the structural behavior of continuous fiber composite materials often takes into account the periodicity of the underlying micro-structure. A well established method dealing with the structural behavior of periodic…

Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning…

This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from noisy data using a combination of sparse regression and weak formulation. Using the…

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…

The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…

Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…

Inverse uncertainty quantification (UQ) tasks such as parameter estimation are computationally demanding whenever dealing with physics-based models, and typically require repeated evaluations of complex numerical solvers. When partial…

The interest in "Physically Unclonable Function"-devices has increased rapidly over the last few years, as they have several interesting properties for system security related applications like, for example, the management of cryptographic…

This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…

Accurate channel impulse response (CIR) modeling in molecular communication (MC) often requires solving coupled reactive diffusion-advection equations, which is computationally expensive for large parameter sweeps or design loops. We…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…