Related papers: NINNs: Nudging Induced Neural Networks
Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…
We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through…
Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…
We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiative tranfer equations.…
Deep Neural Networks (DNNs) have revolutionized a wide range of industries, from healthcare and finance to automotive, by offering unparalleled capabilities in data analysis and decision-making. Despite their transforming impact, DNNs face…
Functions are rich in meaning and can be interpreted in a variety of ways. Neural networks were proven to be capable of approximating a large class of functions[1]. In this paper, we propose a new class of neural networks called "Neural…
Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep…
Deep neural networks (DNNs) have been employed for designing wireless systems in many aspects, say transceiver design, resource optimization, and information prediction. Existing works either use the fully-connected DNN or the DNNs with…
We propose Impatient Deep Neural Networks (DNNs) which deal with dynamic time budgets during application. They allow for individual budgets given a priori for each test example and for anytime prediction, i.e., a possible interruption at…
Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be…
As a method of universal approximation deep neural networks (DNNs) are capable of finding approximate solutions to problems posed with little more constraints than a suitably-posed mathematical system and an objective function.…
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…
Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…
Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique…
We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function…
Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…
We propose a new physics-informed neural network framework, IDPINN, based on the enhancement of initialization and domain decomposition to improve prediction accuracy. We train a PINN using a small dataset to obtain an initial network…
$\textbf{Formal version available at}$ https://cell.com/patterns/fulltext/S2666-3899(23)00200-3 Networks of spiking neurons underpin the extraordinary information-processing capabilities of the brain and have become pillar models in…
Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…
We propose a fast, non-Bayesian method for producing uncertainty scores in the output of pre-trained deep neural networks (DNNs) using a data-driven interval propagating network. This interval neural network (INN) has interval valued…