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Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…

Designing appropriate variational regularization schemes is a crucial part of solving inverse problems, making them better-posed and guaranteeing that the solution of the associated optimization problem satisfies desirable properties.…

Downward continuation is a critical task in potential field processing, including gravity and magnetic fields, which aims to transfer data from one observation surface to another that is closer to the source of the field. Its effectiveness…

Defect detection is a basic and essential task in automatic parts production, especially for automotive engine precision parts. In this paper, we propose a new idea to construct a deep convolutional network combining related knowledge of…

In this work we systematically analyze general properties of differential equations used as machine learning models. We demonstrate that the gradient of the loss function with respect to to the hidden state can be considered as a…

We propose a novel neural network architecture, SwitchNet, for solving the wave equation based inverse scattering problems via providing maps between the scatterers and the scattered field (and vice versa). The main difficulty of using a…

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…

Inverse rendering aims to reconstruct the scene properties of objects solely from multiview images. However, it is an ill-posed problem prone to producing ambiguous estimations deviating from physically accurate representations. In this…

A novel approach is presented for the solution of instantaneous chemical equilibrium problems. The chemical equilibrium can be considered, due to its intrinsically local character, as a mapping of the three-dimensional parameter space…

Discovering the underlying behavior of complex systems is an important topic in many science and engineering disciplines. In this paper, we propose a novel neural network framework, finite difference neural networks (FDNet), to learn…

Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…

Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…

We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…

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…

We present an efficient, effective, and generic approach towards solving inverse problems. The key idea is to leverage the feedback signal provided by the forward process and learn an iterative update model. Specifically, at each iteration,…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

Learning deep representations to solve complex machine learning tasks has become the prominent trend in the past few years. Indeed, Deep Neural Networks are now the golden standard in domains as various as computer vision, natural language…