Physics-Informed Neural Operators (PINOs) are specialized neural networks designed to learn operators of partial differential equations (PDEs) directly from data while incorporating known physical laws. These neural networks aim to bridge the gap between data-driven models and physics-based models. Here are some key features: 1. **Data Integration**: PINOs use available data to learn and generalize the underlying physics of a problem. 2. **Physical Constraints**: Physical laws, often in the form of PDEs, are incorporated into the neural network architecture or loss function, ensuring the model's outputs adhere to known physics. 3. **Generalization**: Unlike traditional neural networks, PINOs are designed to generalize well over a broader range of conditions, due to the incorporation of physical principles. 4. **Interpretable Models**: By using known physical laws, PINOs can be more interpretable than standard neural networks, offering insights into the underlying processes. 5. **Efficiency**: PINOs can be computationally efficient for solving complex physical systems where traditional numerical methods may be infeasible. 6. **Applications**: Suitable for various scientific computing tasks such as fluid dynamics, heat transfer, and quantum mechanics. 7. **Model Complexity**: Can deal with non-linear and high-dimensional problems effectively. 8. **Noise Tolerance**: Physical constraints can help the network to be more resilient to noise in the data. ---- Reference Papers: 1. https://arxiv.org/abs/2111.03794 2. https://iopscience.iop.org/article/10.1088/2632-2153/acd168 3. https://arxiv.org/abs/2207.05748 4. https://docs.nvidia.com/deeplearning/modulus/modulus-v2209/user_guide/neural_operators/darcy_pino.html 5. ["Physics-Informed Neural Operators for Data-Driven Discovery of Nonlinear Partial Differential Equations"](https://www.sciencedirect.com/science/article/pii/S0021999121007227)