Related papers: Two neural-network-based methods for solving obsta…

Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…

In this work we approach the Schr\"odinger equation in quantum wells with arbitrary potentials, using the machine learning technique. Two neural networks with different architectures are proposed and trained using a set of potentials,…

We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic…

Graph neural networks have been successful in many learning problems and real-world applications. A recent line of research explores the power of graph neural networks to solve combinatorial and graph algorithmic problems such as subgraph…

Neural networks based on metric recognition methods have a strictly determined architecture. Number of neurons, connections, as well as weights and thresholds values are calculated analytically, based on the initial conditions of tasks:…

The problem of neural network association is to retrieve a previously memorized pattern from its noisy version using a network of neurons. An ideal neural network should include three components simultaneously: a learning algorithm, a large…

Identifying the obstacle space is crucial for path planning. However, generating an accurate obstacle space remains a significant challenge due to various sources of uncertainty, including motion, behavior, and perception limitations. Even…

Designing mechanically efficient geometry for architectural structures like shells, towers, and bridges, is an expensive iterative process. Existing techniques for solving such inverse problems rely on traditional optimization methods,…

Graph neural networks (GNNs) are increasingly applied to hard optimization problems, often claiming superiority over classical heuristics. However, such claims risk being unsolid due to a lack of standard benchmarks on truly hard instances.…

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…

Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

This paper proposes two efficient approximation methods to solve high-dimensional fully nonlinear partial differential equations (NPDEs) and second-order backward stochastic differential equations (2BSDEs), where such high-dimensional fully…

Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…

Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…

We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…

In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are…

Computational intractability has for decades motivated the development of a plethora of methodologies that mainly aimed at a quality-time trade-off. The use of Machine Learning techniques has finally emerged as one of the possible tools to…