AI/ML+Physics Part 3: Designing an Architecture

Lagrangian neural networks and Hamiltonian neural networks are a good example of the intersection of architecture and loss function. If a system conserves energy or has a mechanical structure, Lagrangian and Hamiltonian systems can be incorporated into both the architecture and loss function to train the neural network. This area of research includes Lagrangian neural networks, deep Operator networks, and Operator networks in general, such as deep UNets and Fourier neural operators. These custom architectures can accelerate training with less data due to physical implicit assumptions. Neural operators are another popular architecture in this field.