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Potential flow is a theoretical model that describes the movement of a fluid, e.g., water or air in situations where viscosity and turbulence are assumed to be negligible. This type of flow is often used as an idealized model to describe the ...

Deep learning techniques have significantly impacted fields such as image processing, computer vision, and natural language processing. However, their influence on quantitative finance, particularly in option pricing, hedging, and portfolio management, ...

Recent advancements in deep learning have significantly improved brain tumour segmentation techniques; however, the results still lack confidence and robustness as they solely consider image data without biophysical priors or pathological ...

Physics-informed Neural Networks (PINNs), a class of neural models that are trained by minimizing a combination of the residual of the governing partial differential equation and the initial and boundary data, have gained immense popularity in the ...

In this paper, we consider a training of Physics Informed Neural Networks with fully connected neural networks for approximation of solutions of one-dimensional advection-diffusion problem. In this context, the neural network is interpreted as a ...${}_{}{}_{\mathrm{}}{}_{\mathrm{}}{}_{\mathrm{}}\mathrm{}\mathrm{}{}_{\mathrm{}}{}_{}$${}_{}$${}_{}$$$${}_{}$${}_{}{\mathcal{}}_{}$

Computational electromagnetics plays a crucial role across diverse domains, notably in fields such as antenna design and radar signature prediction, owing to the omnipresence of electromagnetic phenomena. Numerical methods have replaced ...

Physics-Informed Neural Networks (PINNs) are a promising application of deep neural networks for the numerical solution of nonlinear partial differential equations (PDEs). However, it has been observed that standard PINNs may not be able to ...${}_{}$${}_{}$

We present a new mathematical framework for solution of Partial Differential Equations (PDEs), which is based on an exact transformation of the underlying PDE that removes the boundary constraints from the solution state and moves them into the ...

• A new numerical methodology for solution of partial differential equations is developed.
• A new methodology is based on partial integral equation (PIE) framework.
• A methodology allows to enforce boundary conditions analytically, ...

Solving partial differential equations (PDEs) is a frequent necessity in numerous domains, ranging from complex systems simulation to financial derivatives pricing and continuous-time optimisation tasks. The challenging nature of PDEs, especially in ...

This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on image classification task, it ...

With well-selected data, homogeneous diffusion inpainting can reconstruct images from sparse data with high quality. While 4K colour images of size $3840\times 2160$ can already be inpainted in real time, optimising the known data for applications like ...

Metastases to the lung are a therapeutic challenge because some are fast-evolving while others evolve slowly. Any insight that can be provided for which nodule has to be treated first would help clinicians. In this work, we evaluate the ...

Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the ...

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, ...

• Unsupervised convergence of PDE based document image binarization.
• Robust to ...

Partial differential equations have recently been established as a viable framework for image processing, particularly for image binarization. One drawback of this framework is the requirement for manual parameter tuning. In this work ...

Numerous scientific-computational domains make use of array data. The core computing of the numerical methods and the algorithms involved is related to multi-dimensional array manipulation. Memory layout and the access patterns of that data are crucial ...

This paper studies the 3D reconstruction of a deformable surface from a single image and a reference surface, known as the template. This problem is known as Shape-from-Template and has been recently shown to be well-posed for isometric deformations, ...

We derive a combined analytical and numerical scheme to solve the 1+1-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the ...

Shape recovery based on shading variations of a lighted object was recently revisited with improvements that allow for the photometric stereo approach to serve as a competitive alternative for other shape reconstruction methods. However, most efforts of ...

Reconstruction of 3D objects Based on images is useful in many applications. One of the methods Based on multi-image data is the Photometric Stereo technique relying on several photographs of the observed object from the same point of view, each one ...