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While machine learning models are typically trained to solve prediction problems, we might often want to use them for optimization problems. For example, given a dataset of proteins and their corresponding fluorescence levels, we might want…

The goal of this paper is to analyze and predict the central deflection, natural frequency, and critical buckling load of the multi-directional functionally graded (FG) plate with variable thickness resting on an elastic Winkler foundation.…

We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly…

Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…

This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…

Neural operators are a new type of models that can map between function spaces, allowing trained models to emulate the solution operators of partial differential equations (PDEs). This paper proposes a multigrid Fourier neural operator…

High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…

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…

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that…

Fourier Neural Operator (FNO) is a popular operator learning framework. It not only achieves the state-of-the-art performance in many tasks, but also is efficient in training and prediction. However, collecting training data for the FNO can…

In the presented work, we propose to apply the framework of graph neural networks (GNNs) to predict the dynamics of a rolling element bearing. This approach offers generalizability and interpretability, having the potential for scalable use…

Thermal management in 3D ICs is increasingly challenging due to higher power densities. Traditional PDE-solving-based methods, while accurate, are too slow for iterative design. Machine learning approaches like FNO provide faster…

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…

Accurately predicting long-horizon molecular dynamics (MD) trajectories remains a significant challenge, as existing deep learning methods often struggle to retain fidelity over extended simulations. We hypothesize that one key factor…

We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a…

Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential…

In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random FNO from an edge of chaos perspective. Our investigation…

In this paper, we propose a novel data augmentation method for training neural networks for Direction of Arrival (DOA) estimation. This method focuses on expanding the representation of the DOA subspace of a dataset. Given some input data,…

In this paper, we develop a convolutional neural network model to predict the mechanical properties of a two-dimensional checkerboard composite quantitatively. The checkerboard composite possesses two phases, one phase is soft and ductile…

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…