English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper proposes a novel neural network framework, denoted as spectralintegrated neural networks (SINNs), for resolving three-dimensional forward andinverse dynamic problems. In the SINNs, the spectral integration method isapplied to perform temporal discretization, and then a fully connected neuralnetwork is adopted to solve resulting partial differential equations (PDEs) inthe spatial domain. Specifically, spatial coordinates are employed as inputs inthe network architecture, and the output layer is configured with multipleoutputs, each dedicated to approximating solutions at different time instancescharacterized by Gaussian points used in the spectral method. By leveraging theautomatic differentiation technique and spectral integration scheme, the SINNsminimize the loss function, constructed based on the governing PDEs andboundary conditions, to obtain solutions for dynamic problems. Additionally, weutilize polynomial basis functions to expand the unknown function, aiming toenhance the performance of SINNs in addressing inverse problems. The conceivedframework is tested on six forward and inverse dynamic problems, involvingnonlinear PDEs. Numerical results demonstrate the superior performance of SINNsover the popularly used physics-informed neural networks in terms ofconvergence speed, computational accuracy and efficiency. It is also noteworthythat the SINNs exhibit the capability to deliver accurate and stable solutionsfor long-time dynamic problems.

Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems