Related papers: Predicting nonlinear optical scattering with physi…

Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…

The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such…

The rapid scaling of deep neural networks comes at the cost of unsustainable power consumption. While optical neural networks offer an alternative, their capabilities remain constrained by the lack of efficient optical nonlinearities. To…

We investigate how a residual network can learn to predict the dynamics of interacting shapes purely as an image-to-image regression task. With a simple 2d physics simulator, we generate short sequences composed of rectangles put in motion…

Neural networks have emerged as a powerful way to approach many practical problems in quantum physics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantum many-body system, where the training is…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…

Algorithmic X-ray scatter compensation is a desirable technique in flat-panel X-ray imaging and cone-beam computed tomography. State-of-the-art U-net based image translation approaches yielded promising results. As there are no physics…

A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear…

In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr\"odinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse…

Retrieving accurate 3D reconstructions of objects from the way they reflect light is a very challenging task in computer vision. Despite more than four decades since the definition of the Photometric Stereo problem, most of the literature…

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides…

A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For…

A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential…

The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…

The application of deep learning techniques using convolutional neural networks to the classification of particle collisions in High Energy Physics is explored. An intuitive approach to transform physical variables, like momenta of…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…

Nonlinear materials are often difficult to model with classical state model theory because they have a complex and sometimes inaccurate physical and mathematical description or we simply do not know how to describe such materials in terms…

Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure -- a binary classification task that uses a deep fully-connected neural network to classify…