Related papers: Can physical information aid the generalization ab…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…
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…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…
Solving partial differential equations (PDEs) is an important yet challenging task in fluid mechanics. In this study, we embed an improved Fourier series into neural networks and propose a physics-informed Fourier basis neural network…
Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
This paper introduces a physics-informed machine learning approach for pathloss prediction. This is achieved by including in the training phase simultaneously (i) physical dependencies between spatial loss field and (ii) measured pathloss…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…
Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…
Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…
Deep neural networks (DNNs) have achieved exceptional performance across various fields by learning complex, nonlinear mappings from large-scale datasets. However, they face challenges such as high memory requirements and computational…
We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
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…