Phase-field method (PFM) has become a mainstream computational method for predicting
the evolution of nano and mesoscopic microstructures and properties during materials …

Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

Deep learning surrogate models have shown promise in solving partial differential
equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy …

The classical development of neural networks has primarily focused on learning map**s
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

Abstract 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 …

Neural operators map multiple functions to different functions, possibly in different spaces,
unlike standard neural networks. Hence, neural operators allow the solution of parametric …

Learning partial differential equations'(PDEs) solution operators is an essential problem in
machine learning. However, there are several challenges for learning operators in practical …

Recent advances of data-driven machine learning have revolutionized fields like computer
vision, reinforcement learning, and many scientific and engineering domains. In many real …

Vision transformers have delivered tremendous success in representation learning. This is
primarily due to effective token mixing through self attention. However, this scales …

Geologic carbon sequestration (GCS) is a safety-critical technology that aims to reduce the
amount of carbon dioxide in the atmosphere, which also places high demands on reliability …