Related papers: Physics-informed deep learning for flow and deform…

Permeability is a central concept in the macroscopic description of flow through porous media, with applications spanning from oil recovery to hydrology. Traditional methods for determining the permeability tensor involving flow simulations…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

We demonstrate that embedding physics-driven constraints into machine learning process can dramatically improve accuracy and generalizability of the resulting model. Physics-informed learning is illustrated on the example of analysis of…

Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…

We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge…

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…

High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete…

We show that the error achievable using physics-informed neural networks for solving systems of differential equations can be substantially reduced when these networks are trained using meta-learned optimization methods rather than to using…

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…

A successful deep learning network is highly dependent not only on the training dataset, but the training algorithm used to condition the network for a given task. The loss function, dataset, and tuning of hyperparameters all play an…

Physics-Informed Neural Networks (PINNs) integrate physical principles into machine learning, finding wide applications in various science and engineering fields. However, solving nonlinear hyperbolic partial differential equations (PDEs)…

In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…

Physics-based simulation for fluid flow in porous media is a computational technology to predict the temporal-spatial evolution of state variables (e.g. pressure) in porous media, and usually requires high computational expense due to its…

For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can…

Probabilistic deep learning is deep learning that accounts for uncertainty, both model uncertainty and data uncertainty. It is based on the use of probabilistic models and deep neural networks. We distinguish two approaches to probabilistic…

Recently deep learning and machine learning approaches have been widely employed for various applications in acoustics. Nonetheless, in the area of sound field processing and reconstruction classic methods based on the solutions of wave…

Direct pore-scale simulations of fluid flow through porous media are computationally expensive to perform for realistic systems. Previous works have demonstrated using the geometry of the microstructure of porous media to predict the…

Deep learning method has attracted tremendous attention to handle fluid dynamics in recent years. However, the deep learning method requires much data to guarantee the generalization ability and the data of fluid dynamics are deficient.…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…