Related papers: Muti-Fidelity Prediction and Uncertainty Quantific…

A Fourier neural operator (FNO) is one of the physics-inspired machine learning methods. In particular, it is a neural operator. In recent times, several types of neural operators have been developed, e.g., deep operator networks, Graph…

The UNet-enhanced Fourier Neural Operator (UFNO) extends the Fourier Neural Operator (FNO) by incorporating a parallel UNet pathway, enabling the retention of both high- and low-frequency components. While UFNO improves predictive accuracy…

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…

Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…

A leading family of algorithms for state estimation in dynamic systems with multiple sub-states is based on particle filters (PFs). PFs often struggle when operating under complex or approximated modelling (necessitating many particles)…

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…

Stability analysis of switched systems, characterized by multiple operational modes and switching signals, is challenging due to their nonlinear dynamics. While frameworks such as multiple Lyapunov functions (MLF) provide a foundation for…

Multi-fidelity machine learning methods address the accuracy-efficiency trade-off by integrating scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy…

Magnetotelluric (MT) forward modeling is fundamental for improving the accuracy and efficiency of MT inversion. Neural operators (NOs) have been effectively used for rapid MT forward modeling, demonstrating their promising performance in…

This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…

We propose a novel neural preconditioned Newton (NP-Newton) method for solving parametric nonlinear systems of equations. To overcome the stagnation or instability of Newton iterations caused by unbalanced nonlinearities, we introduce a…

Estimating failure probability is a key task in the field of uncertainty quantification. In this domain, importance sampling has proven to be an effective estimation strategy; however, its efficiency heavily depends on the choice of the…

Laplace approximations are classic, computationally lightweight means for constructing Bayesian neural networks (BNNs). As in other approximate BNNs, one cannot necessarily expect the induced predictive uncertainty to be calibrated. Here we…

Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in…

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Neural operators provide fast surrogate models for time-dependent partial differential equations, but their standard autoregressive use usually assumes that the instantaneous field $u(t,\cdot)$ is a complete state. This assumption fails for…

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…

A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This…

Multi-objective optimization (MOO) exists extensively in machine learning, and aims to find a set of Pareto-optimal solutions, called the Pareto front, e.g., it is fundamental for multiple avenues of research in federated learning (FL).…

Various neural network architectures are used in many of the state-of-the-art approaches for real-time nonlinear state estimation. With the ever-increasing incorporation of these data-driven models into the estimation domain, model…