Related papers: Physics-informed Neural Networks for Solving Inver…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

We use physics-informed neural networks for solving the shallow-water equations for tsunami modeling. Physics-informed neural networks are an optimization based approach for solving differential equations that is completely meshless. This…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

We study the role of an essential hyper-parameter that governs the training of Transformers for neural machine translation in a low-resource setting: the batch size. Using theoretical insights and experimental evidence, we argue against the…

Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving inverse problems, especially in cases where no complete information about the system is known and scatter measurements are available. This is especially…

Modern deep neural network training is typically based on mini-batch stochastic gradient optimization. While the use of large mini-batches increases the available computational parallelism, small batch training has been shown to provide…

Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some…

Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…

We propose a physics-informed neural network as the forward model for tomographic reconstructions of biological samples. We demonstrate that by training this network with the Helmholtz equation as a physical loss, we can predict the…

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

Regular physics-informed neural networks (PINNs) predict the solution of partial differential equations using sparse labeled data but only over a single domain. On the other hand, fully supervised learning models are first trained usually…

Inverse problems are extensively studied in applied mathematics, with applications ranging from acoustic tomography for medical diagnosis to geophysical exploration. Physics informed neural networks (PINNs) have emerged as a powerful tool…

In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully…

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

In this study, we consider classification problems based on neural networks in data-imbalanced environment. Learning from an imbalanced data set is one of the most important and practical problems in the field of machine learning. A…

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

The numerical approximation of solutions to the compressible Euler and Navier-Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been…