Related papers: Harnessing AI for Inverse Partial Differential Equ…

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Introduction: Artificial intelligence (AI) is exhibiting tremendous potential to reduce the massive costs and long timescales of drug discovery. There are however important challenges currently limiting the impact and scope of AI models.…

In this paper we focus on learning optimized partial differential equation (PDE) models for image filtering. In this approach, the grey-scaled images are represented by a vector field of two real-valued functions and the image restoration…

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…

Multimodal artificial intelligence (AI) integrates diverse types of data via machine learning to improve understanding, prediction, and decision-making across disciplines such as healthcare, science, and engineering. However, most…

Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize…

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a…

AI technologies, including deep learning, large-language models have gone from one breakthrough to the other. As a result, we are witnessing growing excitement in robotics at the prospect of leveraging the potential of AI to tackle some of…

Physics-based differentiable rendering (PBDR) has become an efficient method in computer vision, graphics, and machine learning for addressing an array of inverse problems. PBDR allows patterns to be generated from perceptions which can be…

Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…

We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…

We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3], [4]) for solving ill-posed reconstruction problems modeled by PDE's. We consider linear time dependent problems of elliptic, hyperbolic and parabolic types. Each…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this paper, we show that these results can be combined to obtain…

Artificial intelligence (AI) has become a crucial instrument for streamlining processes in various industries, including electrical power systems, as a result of recent digitalization. Algorithms for artificial intelligence are data-driven…

Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…

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…