Related papers: A Parametric Level Set Method for Topology Optimiz…

Deep neural networks (DNNs) have been increasingly deployed on and integrated with edge devices, such as mobile phones, drones, robots and wearables. To run DNN inference directly on edge devices (a.k.a. edge inference) with a satisfactory…

Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…

This paper discusses level set-based structural optimization. Level set-based structural optimization is a method used to determine an optimal configuration for minimizing an objective functional by updating level set functions…

We propose a novel approach for image segmentation that combines Neural Ordinary Differential Equations (NODEs) and the Level Set method. Our approach parametrizes the evolution of an initial contour with a NODE that implicitly learns from…

Neural Networks (NNs) can be used to solve Ordinary and Partial Differential Equations (ODEs and PDEs) by redefining the question as an optimization problem. The objective function to be optimized is the sum of the squares of the PDE to be…

A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…

A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…

A Deep Neural Network (DNN) based algorithm is proposed for the detection and classification of faults in industrial plants. The proposed algorithm has the ability to classify faults, especially incipient faults that are difficult to detect…

Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology…

We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Intensive research has been conducted on the verification and validation of deep neural networks (DNNs), aiming to understand if, and how, DNNs can be applied to safety critical applications. However, existing verification and validation…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

Deep learning based methods hold state-of-the-art results in low-level image processing tasks, but remain difficult to interpret due to their black-box construction. Unrolled optimization networks present an interpretable alternative to…

As a method of universal approximation deep neural networks (DNNs) are capable of finding approximate solutions to problems posed with little more constraints than a suitably-posed mathematical system and an objective function.…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…