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PHYSICS-INFORMED NEURAL NETWORKS

Partial differential equations (PDEs) underlie much of the natural world and are ubiquitous in engineering and scientific modeling. Obtaining accurate and precise solutions to PDEs is an important and notoriously difficult / expensive problem.

PHYSICS-INFORMED NEURAL NETWORKS
PHYSICS-INFORMED NEURAL NETWORKS
PHYSICS-INFORMED NEURAL NETWORKS PHYSICS-INFORMED NEURAL NETWORKS

To build the PDEs into the loss function, partial derivatives of the prediction with respect to the input data are calculated by automatic differentiation. Calculated in this way, the depth of the computation graph grows exponentially in the order of the PDEs.

Loss function Loss Function
computation graphs
computation graphs

These deep computation graphs are well-suited to dataflow architecture. Instead of proceeding kernel by kernel through the computation graph (slow), SambaNova Reconfigurable Dataflow Units™ (RDUs) allow for data to be pipelined, enabling high compute utilization / faster training / etc.

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