Related papers: Polynomial-Augmented Neural Networks (PANNs) with …
The need for consistent treatment of uncertainty has recently triggered increased interest in probabilistic deep learning methods. However, most current approaches have severe limitations when it comes to inference, since many of these…
Deep neural networks and other deep learning methods have very successfully been applied to the numerical approximation of high-dimensional nonlinear parabolic partial differential equations (PDEs), which are widely used in finance,…
Traditionally, an artificial neural network (ANN) is trained slowly by a gradient descent algorithm such as the backpropagation algorithm since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. To…
We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…
Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
Deep Neural Networks (DNNs) have improved the accuracy of classification problems in lots of applications. One of the challenges in training a DNN is its need to be fed by an enriched dataset to increase its accuracy and avoid it suffering…
Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…
The recent success of deep neural networks (DNNs) for function approximation in reinforcement learning has triggered the development of Deep Reinforcement Learning (DRL) algorithms in various fields, such as robotics, computer games,…
Sum-Product Networks (SPNs) are hierarchical, graphical models that combine benefits of deep learning and probabilistic modeling. SPNs offer unique advantages to applications demanding exact probabilistic inference over high-dimensional,…
Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…
The recent development of Physics-Augmented Neural Networks (PANN) opens new opportunities for modeling material behaviors. These approaches have demonstrated their efficiency when trained on synthetic cases. This study aims to demonstrate…
Deep neural networks (DNNs) have become a widely deployed model for numerous machine learning applications. However, their fixed architecture, substantial training cost, and significant model redundancy make it difficult to efficiently…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
Given an existing trained neural network, it is often desirable to learn new capabilities without hindering performance of those already learned. Existing approaches either learn sub-optimal solutions, require joint training, or incur a…
We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we realise a variational formulation, solving a vast class of…
Despite being effective in many application areas, Deep Neural Networks (DNNs) are vulnerable to being attacked. In object recognition, the attack takes the form of a small perturbation added to an image, that causes the DNN to misclassify,…
Deep Neural Networks (DNNs) are rapidly being applied to safety-critical domains such as drone and airplane control, motivating techniques for verifying the safety of their behavior. Unfortunately, DNN verification is NP-hard, with current…