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The Convolutional Neural Networks (CNNs) have been the dominant and effective approach for general computer vision tasks. Recently, Kolmogorov-Arnold neural networks (KANs), based on the Kolmogorov-Arnold representation theorem, have shown…
As function approximators, deep neural networks have served as an effective tool to represent various signal types. Recent approaches utilize multi-layer perceptrons (MLPs) to learn a nonlinear mapping from a coordinate to its corresponding…
Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…
Large-scale mobile traffic analytics is becoming essential to digital infrastructure provisioning, public transportation, events planning, and other domains. Monitoring city-wide mobile traffic is however a complex and costly process that…
We study the numerical approximation of singularly perturbed convection-diffusion problems on one-dimensional pipe networks. In the vanishing diffusion limit, the number and type of boundary conditions and coupling conditions at network…
Convolutional neural networks (CNNs) are inherently suffering from massively redundant computation (FLOPs) due to the dense connection pattern between feature maps and convolution kernels. Recent research has investigated the sparse…
In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of…
As deep neural networks (DNNs) grow in complexity and size, the resultant increase in communication overhead during distributed training has become a significant bottleneck, challenging the scalability of distributed training systems.…
Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers…
We present a diffusion-based approach to quadrupedal locomotion that simultaneously addresses the limitations of learning and interpolating between multiple skills and of (modes) offline adapting to new locomotion behaviours after training.…
Deep convolutional neural networks (CNNs) have brought breakthroughs in processing clinical electrocardiograms (ECGs), speaker-independent speech and complex images. However, typical CNNs require a fixed input size while it is common to…
Physics-informed neural networks and Physics-informed DeepONet excel in solving partial differential equations; however, they often fail to converge for singularly perturbed problems. To address this, we propose two novel frameworks,…
Diffractive deep neural network (DNNet) is a novel machine learning framework on the modulation of optical transmission. Diffractive network would get predictions at the speed of light. It's pure passive architecture, no additional power…
This work presents a novel hybrid approach that integrates Deep Operator Networks (DeepONet) with the Neural Tangent Kernel (NTK) to solve complex inverse problem. The method effectively addresses tasks such as source localization governed…
Learning from 3D point-cloud data has rapidly gained momentum, motivated by the success of deep learning on images and the increased availability of 3D~data. In this paper, we aim to construct anisotropic convolution layers that work…
Extrapolation remains a grand challenge in deep neural networks across all application domains. We propose an operator learning method to solve time-dependent partial differential equations (PDEs) continuously and with extrapolation in time…
Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
We introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. DAOE is based on evolving observables in the Heisenberg…
Accurate localization is a critical requirement for most robotic tasks. The main body of existing work is focused on passive localization in which the motions of the robot are assumed given, abstracting from their influence on sampling…