Related papers: Improved generalization with deep neural operators…

We present polynomial-augmented neural networks (PANNs), a novel machine learning architecture that combines deep neural networks (DNNs) with a polynomial approximant. PANNs combine the strengths of DNNs (flexibility and efficiency in…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN)…

Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing complex physical behavior governed by differential equations.…

We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator…

Deep neural network approximation of nonlinear operators, commonly referred to as DeepONet, has proven capable of approximating PDE backstepping designs in which a single Goursat-form PDE governs a single feedback gain function. In boundary…

Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

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…

Digital network twin (DNT) is a promising paradigm to replicate real-world cellular networks toward continual assessment, proactive management, and what-if analysis. Existing discussions have been focusing on using only deep learning…

We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal…

Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Current groundwater models face a significant challenge in their implementation due to heavy computational burdens. To overcome this, our work proposes a cost-effective emulator that efficiently and accurately forecasts the impact of…

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

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…

Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and…