Related papers: Imbedding Deep Neural Networks
In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…
Neural ordinary differential equations (Neural ODEs) define continuous time dynamical systems with neural networks. The interest in their application for modelling has sparked recently, spanning hybrid system identification problems and…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…
Deep neural networks can be effective means to automatically classify aerial images but is easy to overfit to the training data. It is critical for trained neural networks to be robust to variations that exist between training and test…
Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically…
We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to…
A key attribute that drives the unprecedented success of modern Recurrent Neural Networks (RNNs) on learning tasks which involve sequential data, is their ability to model intricate long-term temporal dependencies. However, a well…
The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive…
Stochastic control problems with delay are challenging due to the path-dependent feature of the system and thus its intrinsic high dimensions. In this paper, we propose and systematically study deep neural networks-based algorithms to solve…
We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…
Deep neural networks (DNNs) have recently achieved impressive success across a wide range of real-world vision and language processing tasks, spanning from image classification to many other downstream vision tasks, such as object…
Sophisticated multilayer neural networks have achieved state of the art results on multiple supervised tasks. However, successful applications of such multilayer networks to control have so far been limited largely to the perception portion…
Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters,…
Neural Ordinary Differential Equations (NODEs) are a novel neural architecture, built around initial value problems with learned dynamics which are solved during inference. Thought to be inherently more robust against adversarial…
In this paper, we address the adversarial training of neural ODEs from a robust control perspective. This is an alternative to the classical training via empirical risk minimization, and it is widely used to enforce reliable outcomes for…
Implicit equilibrium models, i.e., deep neural networks (DNNs) defined by implicit equations, have been becoming more and more attractive recently. In this paper, we investigate an emerging question: can an implicit equilibrium model's…
Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…
Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…