<ul data-eligibleForWebStory="true"><li>Mechanistic PDE Networks is a model for discovering governing partial differential equations from data.</li><li>It represents spatiotemporal data as space-time dependent linear partial differential equations in neural network hidden representations.</li><li>The PDEs represented are solved and decoded for specific tasks, expressing spatiotemporal dynamics in data in neural network hidden space.</li><li>Solving the PDE representations in a compute and memory-efficient manner is a key challenge.</li><li>A native, GPU-capable, parallel, sparse, and differentiable multigrid solver is developed for linear PDEs within Mechanistic PDE Networks.</li><li>This solver acts as a module to handle linear PDEs efficiently.</li><li>The architecture can discover nonlinear PDEs in complex scenarios while being robust to noise, leveraging the PDE solver.</li><li>PDE discovery is validated on various equations including reaction-diffusion and Navier-Stokes equations.</li></ul>

Mechanistic PDE Networks for Discovery of Governing Equations

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