Related papers: Numerically Informed Convolutional Operator Networ…
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…
In this paper, we propose neural networks that tackle the problems of stability and field-of-view of a Convolutional Neural Network (CNN). As an alternative to increasing the network's depth or width to improve performance, we propose…
Automated design methods for convolutional neural networks (CNNs) have recently been developed in order to increase the design productivity. We propose a neuroevolution method capable of evolving and optimizing CNNs with respect to the…
In-Context Operator Networks (ICONs) have demonstrated the ability to learn operators across diverse partial differential equations using few-shot, in-context learning. However, existing ICONs process each spatial point as an individual…
This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…
This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified…
Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however…
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…
Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…
We develop a novel framework for uncertainty quantification in operator learning, the Stochastic Operator Network (SON). SON combines the stochastic optimal control concepts of the Stochastic Neural Network (SNN) with the DeepONet. By…
We motivate the use of neural networks for the construction of numerical solutions to differential equations. We prove that there exists a feed-forward neural network that can arbitrarily minimise an objective function that is zero at the…
Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…
In this paper we propose a new method for training neural networks (NNs) for frequency modulated continuous wave (FMCW) radar mutual interference mitigation. Instead of training NNs to regress from interfered to clean radar signals as in…
Focused ultrasound (FUS) therapy is a promising tool for optimally targeted treatment of spinal cord injuries (SCI), offering submillimeter precision to enhance blood flow at injury sites while minimizing impact on surrounding tissues.…
We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where…
Machine-learning algorithms have shown outstanding image recognition or classification performance for computer vision applications. However, the compute and energy requirement for implementing such classifier models for large-scale…
Solving partial differential equations remains a central challenge in scientific machine learning. Neural operators offer a promising route by learning mappings between function spaces and enabling resolution-independent inference, yet they…
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…
Fine-grained recognition is challenging due to its subtle local inter-class differences versus large intra-class variations such as poses. A key to address this problem is to localize discriminative parts to extract pose-invariant features.…