Related papers: Evolutional Deep Neural Network
We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…
Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection…
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a…
Deep neural networks (DNNs) have succeeded in many different perception tasks, e.g., computer vision, natural language processing, reinforcement learning, etc. The high-performed DNNs heavily rely on intensive resource consumption. For…
Deep neural networks (DNN) have been studied in various machine learning areas. For example, event-related potential (ERP) signal classification is a highly complex task potentially suitable for DNN as signal-to-noise ratio is low, and…
Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…
Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering,…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
Many DNN-enabled vision applications constantly operate under severe energy constraints such as unmanned aerial vehicles, Augmented Reality headsets, and smartphones. Designing DNNs that can meet a stringent energy budget is becoming…
In recent years, Deep Learning models have shown a great performance in complex optimization problems. They generally require large training datasets, which is a limitation in most practical cases. Transfer learning allows importing the…
Deep neural networks (DNNs) are widely used in pattern-recognition tasks for which a human comprehensible, quantitative description of the data-generating process, e.g., in the form of equations, cannot be achieved. While doing so, DNNs…
Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce a self-adaptive algorithm: the adaptive network enhancement (ANE) method,…
We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions…
The remarkable success of Deep Neural Networks(DNN) is driven by gradient-based optimization, yet this process is often undermined by its tendency to produce disordered weight structures, which harms feature clarity and degrades learning…
Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…
Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…