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We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…

Deep learning has become a popular tool across many scientific fields, including the study of differential equations, particularly partial differential equations. This work introduces the basic principles of deep learning and the Deep…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…

In typical machine learning tasks and applications, it is necessary to obtain or create large labeled datasets in order to to achieve high performance. Unfortunately, large labeled datasets are not always available and can be expensive to…

We present and compare three approaches for accurately retrieving depth-resolved temperature distributions within materials from their thermal-radiation spectra, based on: (1) a nonlinear equation solver implemented in commercial software,…

The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…

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…

Thermal plasma properties play a critical role in plasma simulations and plasma-related applications. However, their strong nonlinear dependence on temperature, pressure, and gas composition makes accurate and efficient evaluation…

The dynamics of burning plasmas in tokamaks are crucial for advancing controlled thermonuclear fusion. This study applies the NeuralPlasmaODE, a multi-region multi-timescale transport model, to simulate the complex energy transfer processes…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

Deep learning is having a tremendous impact in many areas of computer science and engineering. Motivated by this success, deep neural networks are attracting an increasing attention in many other disciplines, including physical sciences. In…

Many important physical processes have dynamics that are too complex to completely model analytically. Optimisation of such processes often relies on intuition, trial-and-error, or the construction of empirical models. Machine learning…

This paper presents a method to simulate the thermal behavior of 3D systems using a graph neural network. The method discussed achieves a significant speed-up with respect to a traditional finite-element simulation. The graph neural network…

Deep learning is having a profound impact in many fields, especially those that involve some form of image processing. Deep neural networks excel in turning an input image into a set of high-level features. On the other hand, tomography…

Thermal images have various applications in security, medical and industrial domains. This paper proposes a practical deep-learning approach for thermal image classification. Accurate and efficient classification of thermal images poses a…

The electron density is a key parameter to characterize any plasma. Most of the plasma applications and research in the area of low-temperature plasmas (LTPs) are based on the accurate estimations of plasma density and plasma temperature.…

In this paper, we study the linear transport model by adopting the deep learning method, in particular the deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt…