The importance of tensor handling and implementation of physics-informed DeepONets

Key points

• Physics-informed neural networks (PINNs) reduce or eliminate the need for large labelled datasets by enforcing governing equations during training.1
• Despite these advantages, we show that their application to higher-dimensional problems remains limited by the computational cost of training.1
• To address this issue, we propose a modified PI-DeepONet architecture that reduces this cost by removing redundancy in how the Branch network processes input functions across collocation points.1
• These results demonstrate that careful consideration of how PI-DeepONets are implemented can yield substantial gains, enhancing the practical performance of PI-DeepONets and enabling their application to otherwise intractable physics-informed learning problems.1

Sources (1)

• [1]The importance of tensor handling and implementation of physics-informed DeepONets
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 04:22 PM

  Physics-informed Deep Operator Networks (PI-DeepONets) extend this approach to learning solution operators, enabling rapid prediction across families of problems.

  Physics-informed neural networks (PINNs) reduce or eliminate the need for large labelled datasets by enforcing governing equations during training.

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