Related papers: Fourier Neural Operators for Learning Dynamics in …

Capturing the dynamics of quantum many-body systems under time-dependent driving protocols is a central challenge for numerical simulations. Existing methods such as tensor networks and time-dependent neural quantum states, however, must be…

Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…

Data-driven surrogates can replace expensive multiphysics solvers for parametric PDEs, yet building compact, accurate neural operators for three-dimensional problems remains challenging: in Fourier Neural Operators, dense mode-wise spectral…

The great success of Deep Neural Networks (DNNs) has inspired the algorithmic development of DNN-based Fixed-Point (DNN-FP) for computer vision tasks. DNN-FP methods, trained by Back-Propagation Through Time or computing the inaccurate…

Real-time monitoring of induced seismicity is critical to mitigate operational risks, relying on the rapid and accurate classification of triggered data from continuous data streams. Deep learning models are effective for this purpose but…

Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we…

High-fidelity simulations of laser welding capture complex thermo-fluid phenomena, including phase change, free-surface deformation, and keyhole dynamics, however their computational cost limits large-scale process exploration and real-time…

We introduce the Z-Domain Neural Operator (ZNO), a causal neural operator whose layers are stable low-rank multiple-input multiple-output (MIMO) rational filters parameterized directly in the $z$-plane. ZNO addresses a limitation of…

We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…

Multi-scale dynamic wake modeling and prediction are essential for the real-time control and optimization of floating offshore wind turbines (FOWTs). In this study, wakes of FOWTs under coupled surge and pitch motions across a range of…

This study aims to develop surrogate models for accelerating decision making processes associated with carbon capture and storage (CCS) technologies. Selection of sub-surface $CO_2$ storage sites often necessitates expensive and involved…

We introduce sparse autoencoder neural operators (SAE-NOs), a new class of sparse autoencoders that operate in function spaces rather than fixed-dimensional Euclidean representations. We formalize the functional representation hypothesis,…

We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…

Accurate modeling of magnetic hysteresis is essential for high-fidelity power electronics device simulations. The transient hysteresis phenomena such as the ringing effect and the minor loops are the bottleneck for the accurate hysteresis…

Continuum robots enable dexterous manipulation in constrained environments, but require accurate and efficient models for real-time manipulation and control. Traditional physics-based models can be computationally expensive and may suffer…

Flexible intelligent metasurfaces (FIMs) offer a new solution for wireless communications by introducing morphological degrees of freedom, dynamically morphing their three-dimensional shape to ensure multipath signals interfere…

A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For…

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…

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…