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Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations often involve coupled…

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of…

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators…

Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

FNO and DeepONet are by far the most popular neural operator learning algorithms. FNO seems to enjoy an edge in popularity due to its ease of use, especially with high dimensional data. However, a lesser-acknowledged feature of DeepONet is…

Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…

Underground hydrogen storage (UHS) is a promising energy storage option for the current energy transition to a low-carbon economy. Fast modeling of hydrogen plume migration and pressure field evolution is crucial for UHS field management.…

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)…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…

Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is…

PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…

Reliable multiscale models of thrombosis require platelet-scale fidelity at organ-scale cost, a gap that scientific machine learning has the potential to narrow. We train a DeepONet surrogate on platelet dynamics generated with LAMMPS for…

Edge Digital Twins (EDTs) are crucial for monitoring and control of Power Electronics Systems (PES). However, existing modeling approaches struggle to consistently capture continuously evolving hybrid dynamics that are inherent in PES,…

Fast and accurate surrogates for physics-driven partial differential equations (PDEs) are essential in fields such as aerodynamics, porous media design, and flow control. However, many transformer-based models and existing neural operators…

Operator learning has become a powerful tool for accelerating the solution of parameterized partial differential equations (PDEs), enabling rapid prediction of full spatiotemporal fields for new initial conditions or forcing functions.…

Scientific Machine Learning (ML) is gaining momentum as a cost-effective alternative to physics-based numerical solvers in many engineering applications. In fact, scientific ML is currently being used to build accurate and efficient…

Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon dynamical systems. While neural operator methods such as the…

Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as…