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Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…

We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…

Deep neural networks (DNNs) have been widely used to solve partial differential equations (PDEs) in recent years. In this work, a novel deep learning-based framework named Particle Weak-form based Neural Networks (ParticleWNN) is developed…

Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…

The isothermal gas sphere is well known as a powerful tool to model many problems in astrophysics, physics, chemistry, and engineering. This singular differential equation has not an exact solution and solved only by numerical and…

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…

Precipitation results from complex processes across many scales, making its accurate simulation in Earth system models (ESMs) challenging. Existing post-processing methods can improve ESM simulations locally, but cannot correct errors in…

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

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)…

We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…

We propose a new class of physics-informed neural networks, called Physics-Informed Generator-Encoder Adversarial Networks, to effectively address the challenges posed by forward, inverse, and mixed problems in stochastic differential…

The perturbation method is applied to numerical solution of the Lane-Emden Equation of arbitrary index n, and the global parameters of polytropes are found as function of polytropic index n.

This work presents the application of the artificial neural networks, trained and structurally optimized by genetic algorithms, for modeling of crude distillation process at PKN ORLEN S.A. refinery. Models for the main fractionator…

The physical world is governed by the laws of physics, often represented in form of nonlinear partial differential equations (PDEs). Unfortunately, solution of PDEs is non-trivial and often involves significant computational time. With…

Artifical neural networks (ANNs) are universal approximators capable of learning any correlation between arbitrary input data with corresponding outputs, which can also be exploited to represent a low-dimensional chemistry manifold in the…

Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably, whereas some traditional algorithm-based methods are more robust to…

The interpretation of observations of atomic and molecular tracers in the galactic and extragalactic interstellar medium (ISM) requires comparisons with state-of-the-art astrophysical models to infer some physical conditions. Usually, ISM…

Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to…

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…

We compare the Finite Element Method (FEM) simulation of a standard Partial Differential Equation thermal problem of a plate with a hole with a Neural Network (NN) simulation. The largest deviation from the true solution obtained from FEM…