Related papers: Forward and inverse problems for Eikonal equation …

Surface temperature distribution is crucial for thermal property-based studies about irregular asteroids in our Solar System. While direct numerical simulations could model surface temperatures with high fidelity, they often take a…

In this paper, the authors propose a new approach to solving the groundwater flow equation in the Toth basin of arbitrary top and bottom topographies using deep learning. Instead of using traditional numerical solvers, they use a DeepONet…

This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy…

Full waveform inversion (FWI) aims to reconstruct subsurface velocity models from observed seismic wavefields and has recently benefited from advances in deep learning (DL). The performance of DL-based FWI critically depends on the…

Solving inverse problems is a fundamental component of science, engineering and mathematics. With the advent of deep learning, deep neural networks have significant potential to outperform existing state-of-the-art, model-based methods for…

In this paper, we propose a multiscale DeepONet to represent nonlinear operator between Banach spaces of highly oscillatory continuous functions. The multiscale deep neural network (DNN) utilizes a multiple scaling technique to convert high…

We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution…

Imaging problems such as the one in nanoCT require the solution of an inverse problem, where it is often taken for granted that the forward operator, i.e., the underlying physical model, is properly known. In the present work we address the…

To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…

Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information…

The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM)…

The concept of physics-informed neural networks has become a useful tool for solving differential equations due to its flexibility. There are a few approaches using this concept to solve the eikonal equation which describes the…

The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…

Recently, learning equivariant representations has attracted considerable research attention. Dieleman et al. introduce four operations which can be inserted into convolutional neural network to learn deep representations equivariant to…

Data inconsistency leads to a slow training process when deep neural networks are used for the inverse design of photonic devices, an issue that arises from the fundamental property of non-uniqueness in all inverse scattering problems. Here…

Deep learning has been the most popular machine learning method in the last few years. In this chapter, we present the application of deep learning and physics-informed neural networks concerning structural mechanics and vibration problems.…

In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final time data. The unknown potential in this inverse problem is…