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

We study the problem of inferring substitutable and complementary items, which underpins applications such as alternative and follow-up purchase suggestions. Existing approaches typically learn from behavior-derived item-item associations…

The design of structures and vehicles subject to fluid-structure interaction (FSI) often requires high-fidelity coupled analysis. While the design variables pertain to the structure, the computational cost is dominated by the fluid solver,…

The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computational costs involved become prohibitive. On the other hand,…

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…

Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random…

Inverse modeling for computing a high-dimensional spatially-varying property field from indirect sparse and noisy observations is a challenging problem. This is due to the complex physical system of interest often expressed in the form of…

We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby refer to as the surrogate matrix methodology. This methodology is…

Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…

The non-equilibrium dynamics of mesoscale phase transitions are fundamentally shaped by thermal fluctuations, which not only seed instabilities but actively control kinetic pathways, including rare barrier-crossing events such as nucleation…

Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…

This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis…

We propose KO-PDE-IDENT, a data-driven framework for identifying parsimonious partial differential equations (PDEs) with false discovery rate (FDR) control. PDE discovery from noisy observations is often hindered by extreme…

Federated Learning (FL) is an emerging paradigm through which decentralized devices can collaboratively train a common model. However, a serious concern is the leakage of privacy from exchanged gradient information between clients and the…

Metamodeling of complex numerical systems has recently attracted the interest of the mathematical programming community. Despite the progress in high performance computing, simulations remain costly, as a matter of fact, the assessment of…

We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…

Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…

In this article, we introduce and analyze a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realizations of the driving noise process. If applied…

Denoising diffusion models offer a promising approach to accelerating magnetic resonance imaging (MRI) and producing diagnostic-level images in an unsupervised manner. However, our study demonstrates that even tiny worst-case potential…

Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations…

We consider a fully discrete scheme for nonlinear stochastic partial differential equations with non-globally Lipschitz coefficients driven by multiplicative noise in a multi-dimensional setting. Our method uses a polynomial based spectral…