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The inclusion of high-fidelity simulations of SOL turbulence and transient MHD events such as ELMs in highly iterative applications remains computationally prohibitive, limiting their use in design and control workflows. Understanding these…

Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…

Neural operators have emerged as a powerful, data-driven paradigm for learning solution operators of partial differential equations (PDEs). State-of-the-art architectures, such as the Fourier Neural Operator (FNO), have achieved remarkable…

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper,…

Accurately capturing the behavior of grain-oriented (GO) ferromagnetic materials is crucial for modeling the electromagnetic devices. In this paper, neural operator models, including Fourier neural operator (FNO), U-net combined FNO (U-FNO)…

We address the problem of predicting spatio-temporal processes with temporal patterns that vary across spatial regions, when data is obtained as a stream. That is, when the training dataset is augmented sequentially. Specifically, we…

Carbon capture and storage (CCS) plays an essential role in global decarbonization. Scaling up CCS deployment requires accurate and high-resolution modeling of the storage reservoir pressure buildup and the gaseous plume migration. However,…

In the literature on stochastic frontier models until the early 2000s, the joint consideration of spatial and temporal dimensions was often inadequately addressed, if not completely neglected. However, from an evolutionary economics…

With an ever-increasing number of sensors in modern society, spatio-temporal time series forecasting has become a de facto tool to make informed decisions about the future. Most spatio-temporal forecasting models typically comprise distinct…

Neural operators learn to map initial conditions to the terminal solution of partial differential equations (PDEs), providing a surrogate for the full operator mapping. This enables rapid prediction across different input configurations.…

Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as…

Predicting the large-scale dynamics of three-dimensional (3D) turbulence is challenging for machine learning approaches. This paper introduces a transformer-based neural operator (TNO) to achieve precise and efficient predictions in the…

Deep neural network models have shown a great potential in accelerating the simulation of fluid dynamic systems. Once trained, these models can make inference within seconds, thus can be extremely efficient. However, they suffer from a…

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

Long-term predictions of nonlinear dynamics of three-dimensional (3D) turbulence are very challenging for machine learning approaches. In this paper, we propose an implicit U-Net enhanced Fourier neural operator (IU-FNO) for stable and…

Climate simulations are essential in guiding our understanding of climate change and responding to its effects. However, it is computationally expensive to resolve complex climate processes at high spatial resolution. As one way to speed up…

Environmental and climate processes are often distributed over large space-time domains. Their complexity and the amount of available data make modelling and analysis a challenging task. Statistical modelling of environment and climate data…

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the…

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical…