Related papers: DeepPropNet -- A Recursive Deep Propagator Neural …
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…
A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions. We rigorously prove,…
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.…
The backpropagation of error algorithm used to train deep neural networks has been fundamental to the successes of deep learning. However, it requires sequential backward updates and non-local computations, which make it challenging to…
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…
Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…
In this paper, we propose a novel network training mechanism called "dynamic channel propagation" to prune the neural networks during the training period. In particular, we pick up a specific group of channels in each convolutional layer to…
We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…
The quality of data representation in deep learning methods is directly related to the prior model imposed on the representations; however, generally used fixed priors are not capable of adjusting to the context in the data. To address this…
Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…
The training of deep neural nets is expensive. We present a predictor- corrector method for the training of deep neural nets. It alternates a predictor pass with a corrector pass using stochastic gradient descent with backpropagation such…
The advancement of deep convolutional neural networks (DCNNs) has driven significant improvement in the accuracy of recognition systems for many computer vision tasks. However, their practical applications are often restricted in…
Originally inspired by neurobiology, deep neural network models have become a powerful tool of machine learning and artificial intelligence, where they are used to approximate functions and dynamics by learning from examples. Here we give a…
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order model, such as a deep neural network, to approximate the…
In this study, we build upon a previously proposed neuroevolution framework to evolve deep convolutional models. Specifically, the genome encoding and the crossover operator are extended to make them applicable to layered networks. We also…
Pointer Network (PtrNet) is a specific neural network for solving Combinatorial Optimization Problems (COPs). While PtrNets offer real-time feed-forward inference for complex COPs instances, its quality of the results tends to be less…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Based on the predictive coding theory in neuroscience, we designed a bi-directional and recurrent neural net, namely deep predictive coding networks (PCN). It has feedforward, feedback, and recurrent connections. Feedback connections from a…
The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…
We propose a Deep Operator Network~(DeepONet) framework to learn the dynamic response of continuous-time nonlinear control systems from data. To this end, we first construct and train a DeepONet that approximates the control system's local…