Related papers: Convolution Operator Network for Forward and Inver…
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…
Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…
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…
Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma…
With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…
This work introduces the quantum-inspired variational convolution (QiVC) framework, a novel learning paradigm that integrates principles of probabilistic inference, variational optimization, and quantum-inspired transformations within…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
Convolutional neural networks are now seeing widespread use in a variety of fields, including image classification, facial and object recognition, medical imaging analysis, and many more. In addition, there are applications such as…
We propose Re-parameterized Refocusing Convolution (RefConv) as a replacement for regular convolutional layers, which is a plug-and-play module to improve the performance without any inference costs. Specifically, given a pre-trained model,…
The pressure Poisson equation (PPE) represents the primary computational bottleneck in fractional step methods for incompressible flow simulations, requiring iterative solutions of large-scale linear systems. We previously introduced HyDEA,…
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…
Plasma systems exhibit complex multiscale dynamics, resolving which poses significant challenges for conventional numerical simulations. Machine learning (ML) offers an alternative by learning data-driven representations of these dynamics.…
Despite the apparent complexity of turbulent flow, identifying a simpler description of the underlying dynamical system remains a fundamental challenge. Capturing how the turbulent flow meanders amongst unstable states (simple invariant…
Designing high-performance substrate-integrated waveguide (SIW) filters with both closely spaced and widely separated resonances is challenging. Consequently, there is a growing need for robust methods that reduce reliance on time-consuming…
Design and analysis of inelastic materials requires prediction of physical responses that evolve under loading. Numerical simulation of such behavior using finite element (FE) approaches can call for significant time and computational…
The success of building a high-resolution velocity model using machine learning is hampered by generalization limitations that often limit the success of the approach on field data. This is especially true when relying on neural operators…
Model-based control methods for robotic systems such as quadrotors, autonomous driving vehicles and flexible manipulators require motion models that generate accurate predictions of complex nonlinear system dynamics over long periods of…
Recent learning-based correction approaches in EPI estimate a displacement field, unwarp the reversed-PE image pair with the estimated field, and average the unwarped pair to yield a corrected image. Unsupervised learning in these…
Vision-language-action (VLA) models have shown great potential in building generalist robots, but still face a dilemma-misalignment of 2D image forecasting and 3D action prediction. Besides, such a vision-action entangled training manner…
We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators acting on discrete multicomponent signals. This result naturally leads to the identification of the Parseval convolution operators as the…