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In this work we explore the advantages of end-to-end learning of multilayer maps offered by feed forward neural-networks (FFNN) for learning and predicting dynamics from transient fluid flow data.While machine learning in general depends on…

In recent years, a plethora of methods combining deep neural networks and partial differential equations have been developed. A widely known and popular example are physics-informed neural networks. They solve forward and inverse problems…

Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…

Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial differential equation (PDE) solving.

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…

The aim of this note is to construct a neural network for which the linear finite element approximation of a simple one dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to…

In modern deep learning, the models are learned by applying gradient updates using an optimizer, which transforms the updates based on various statistics. Optimizers are often hand-designed and tuning their hyperparameters is a big part of…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

Deep learning frameworks have become powerful tools for approaching scientific problems such as turbulent flow, which has wide-ranging applications. In practice, however, existing scientific machine learning approaches have difficulty…

Resampling is a key component of sample-based recursive state estimation in particle filters. Recent work explores differentiable particle filters for end-to-end learning. However, resampling remains a challenge in these works, as it is…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a…

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…

Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…

Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…

Learning to learn is a powerful paradigm for enabling models to learn from data more effectively and efficiently. A popular approach to meta-learning is to train a recurrent model to read in a training dataset as input and output the…

Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning -- a key tool for performing meta-learning -- learns a…

Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. Deep learning is also considered as a powerful tool with high flexibility to approximate functions. In the present work,…

While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which addresses both families of tasks simultaneously. We…