Related papers: DPM: A deep learning PDE augmentation method (with…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…

Deep Matching (DM) is a popular high-quality method for quasi-dense image matching. Despite its name, however, the original DM formulation does not yield a deep neural network that can be trained end-to-end via backpropagation. In this…

In recent years, neural networks have achieved remarkable progress in various fields and have also drawn much attention in applying them on scientific problems. A line of methods involving neural networks for solving partial differential…

Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times,…

We study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for a general class of nonsmooth partial differential equation (PDE)-constrained optimization problems, where…

Computational Fluid Dynamics (CFD) simulations using turbulence models are commonly used in engineering design. Of the different turbulence modeling approaches that are available, eddy viscosity based models are the most common for their…

In this paper, we consider a deep learning approach to the limited aperture inverse obstacle scattering problem. It is well known that traditional deep learning relies solely on data, which may limit its performance for the inverse problem…

Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…

Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but…

Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and…

The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…

Many engineering and scientific fields have recently become interested in modeling terms in partial differential equations (PDEs) with neural networks, which requires solving the inverse problem of learning neural network terms from…

We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…

This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…

Numerical simulation is indispensable in industrial design processes. It can replace expensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement,…

Utilizing physics-informed neural networks (PINN) to solve partial differential equations (PDEs) becomes a hot issue and also shows its great powers, but still suffers from the dilemmas of limited predicted accuracy in the sampling domain…

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…

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…

This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and…