Related papers: Radial Basis Operator Networks
Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an…
Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their…
The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
Radial basis function (RBF) network is a third layered neural network that is widely used in function approximation and data classification. Here we propose a quantum model of the RBF network. Similar to the classical case, we still use the…
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…
The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study…
Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black…
We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative…
Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…
Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…
Many applications, especially in physics and other sciences, call for easily interpretable and robust machine learning techniques. We propose a fully gradient-based technique for training radial basis function networks with an efficient and…
Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…
Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…
Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for…
In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions…
Existing methods for out-of-distribution (OOD) detection use various techniques to produce a score, separate from classification, that determines how ``OOD'' an input is. Our insight is that OOD detection can be simplified by using a neural…
In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…
Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…