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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Deep neural networks are transforming fields ranging from computer vision tocomputational medicine, and we recently extended their application to the fieldof phase-change heat transfer by introducing theory-trained neural networks(TTNs) for a solidification problem \cite{TTN}. Here, we present general,in-depth, and empirical insights into theory-training networks for learning thesolution of highly coupled differential equations. We analyze the deterioratingeffects of the oscillating loss on the ability of a network to satisfy theequations at the training data points, measured by the final training loss, andon the accuracy of the inferred solution. We introduce a theory-trainingtechnique that, by leveraging regularization, eliminates those oscillations,decreases the final training loss, and improves the accuracy of the inferredsolution, with no additional computational cost. Then, we present guidelinesthat allow a systematic search for the network that has the optimal trainingtime and inference accuracy for a given set of equations; following theseguidelines can reduce the number of tedious training iterations in that search.Finally, a comparison between theory-training and the rival, conventionalmethod of solving differential equations using discretization attests to theadvantages of theory-training not being necessarily limited to high-dimensionalsets of equations. The comparison also reveals a limitation of the currenttheory-training framework that may limit its application in domains whereextreme accuracies are necessary.

On Theory-training Neural Networks to Infer the Solution of Highly Coupled Differential Equations