Related papers: Application of Lie Group-based Neural Network Meth…

In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…

In response to the global challenge of mental health problems, we proposes a Logical Neural Network (LNN) based Neuro-Symbolic AI method for the diagnosis of mental disorders. Due to the lack of effective therapy coverage for mental…

Deep neural networks are widely used in practical applications of AI, however, their inner structure and complexity made them generally not easily interpretable. Model transparency and interpretability are key requirements for multiple…

Extracting dynamic models from data is of enormous importance in understanding the properties of unknown systems. In this work, we employ Lipschitz neural networks, a class of neural networks with a prescribed upper bound on their Lipschitz…

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

This article proposes a methodology to model and simulate complex systems, based on IRM4MLS, a generic agent-based meta-model able to deal with multi-level systems. This methodology permits the engineering of dynamic multi-level agent-based…

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…

Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems, e.g., image classification, natural language processing or human action recognition. Although these methods…

Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…

Recently, the use of pre-trained model to build neural network based on transfer learning methodology is increasingly popular. These pre-trained models present the benefit of using less computing resources to train model with smaller amount…

We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the…

The adoption of intelligent systems with Artificial Neural Networks (ANNs) embedded in hardware for real-time applications currently faces a growing demand in fields like the Internet of Things (IoT) and Machine to Machine (M2M). However,…

Machine learning (ML) has been used to develop increasingly accurate link quality estimators for wireless networks. However, more in-depth questions regarding the most suitable class of models, most suitable metrics and model performance on…

The neural linear model is a simple adaptive Bayesian linear regression method that has recently been used in a number of problems ranging from Bayesian optimization to reinforcement learning. Despite its apparent successes in these…

Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close…

The recently introduced locally orderless tensor network (LoTeNet) for supervised image classification uses matrix product state (MPS) operations on grids of transformed image patches. The resulting patch representations are combined back…

A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…