<ul data-eligibleForWebStory="false"><li>Researchers have developed a feedforward neural network based on conservative approximation for WENO schemes in solving hyperbolic conservation laws.</li><li>The neural network replaces the classical WENO weighting procedure by taking point values as inputs and two nonlinear weights as outputs from a three-point stencil.</li><li>Supervised learning is used with a new labeled dataset for conservative approximation, incorporating a symmetric-balancing term in the loss function to ensure high-order accuracy and match the conservative approximation to the derivative.</li><li>The resulting WENO schemes, WENO3-CADNNs, exhibit robust generalization and outperform WENO3-Z while achieving accuracy comparable to WENO5-JS across different benchmark scenarios and resolutions.</li></ul>

Conservative approximation-based feedforward neural network for WENO schemes

Discover more