Related papers: Radial Basis Operator Networks
The study of operator learning involves the utilization of neural networks to approximate operators. Traditionally, the focus has been on single-operator learning (SOL). However, recent advances have rapidly expanded this to include the…
We present a novel framework, called balanced overlay networks (BON), that provides scalable, decentralized load balancing for distributed computing using large-scale pools of heterogeneous computers. Fundamentally, BON encodes the…
Robots can complete all human-performed tasks, but due to their current lack of knowledge, some tasks still cannot be completed by them with a high degree of success. However, with the right knowledge, these tasks can be completed by robots…
An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…
Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…
Deep learning has triggered explosive growth in the demand for specialized hardware processors, thus motivating the development of scalable and reconfigurable computing substrates. Optical processors offer a fundamentally different…
Self-Organized Operational Neural Networks (Self-ONNs) have recently been proposed as new-generation neural network models with nonlinear learning units, i.e., the generative neurons that yield an elegant level of diversity; however, like…
Diffractive optical neural networks (DONNs) have demonstrated unparalleled energy efficiency and parallelism by processing information directly in the optical domain. However, their computational expressivity is constrained by static,…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Operational Neural Networks (ONNs) have recently been proposed to address the well-known limitations and drawbacks of conventional Convolutional Neural Networks (CNNs) such as network homogeneity with the sole linear neuron model. ONNs are…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learning remain…
Random Boolean networks (RBNs) are frequently employed for modelling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive RBN (HARBN) as a system consisting of…
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically…
In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…
Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…
This work considers a single-cell random access channel (RACH) in cellular wireless networks. Communications over RACH take place when users try to connect to a base station during a handover or when establishing a new connection. Within…
Tabular data is the most common data format adopted by our customers ranging from retail, finance to E-commerce, and tabular data classification plays an essential role to their businesses. In this paper, we present Network On Network…
The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…
From fully connected neural networks to convolutional neural networks, the learned parameters within a neural network have been primarily relegated to the linear parameters (e.g., convolutional filters). The non-linear functions (e.g.,…