Related papers: Phase space learning with neural networks
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…
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…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully; however, its convergence is slow and might not be…
This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulated as the evolution of network parameters in an evolution…
Deep neural networks have emerged as effective tools for computational imaging including quantitative phase microscopy of transparent samples. To reconstruct phase from intensity, current approaches rely on supervised learning with training…
In this paper, we propose a domain-decomposition-based deep learning (DL) framework, named transient-CoMLSim, for accurately modeling unsteady and nonlinear partial differential equations (PDEs). The framework consists of two key…
Deep Learning has been widely applied in the area of image processing and natural language processing. In this paper, we propose an end-to-end communication structure based on autoencoder where the transceiver can be optimized jointly. A…
We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…
Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…
We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…
In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…
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…
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…
We use spatially-sparse two, three and four dimensional convolutional autoencoder networks to model sparse structures in 2D space, 3D space, and 3+1=4 dimensional space-time. We evaluate the resulting latent spaces by testing their…
Microstructural evolution is a key aspect of understanding and exploiting the structure-property-performance relation of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles…
Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To…
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…
This paper introduces the Descriptive Variational Autoencoder (DVAE), an unsupervised and end-to-end trainable neural network for predicting vehicle trajectories that provides partial interpretability. The novel approach is based on the…