Hamiltonian Neural Network for Fluid Simulation

The patent applies preliminary action by pre-training the neural network offline using high-fidelity Navier-Stokes simulation data and experimental measurements. This preliminary training phase captures complex fluid dynamics patterns, which are then reused during runtime simulations without requiring repeated expensive computations. The network learns from pre-collected data, enabling fast predictions during actual vehicle design iterations.

The patent uses copying by creating a neural network model that replicates the behavior of complex physical fluid dynamics models. Instead of repeatedly executing computationally intensive Navier-Stokes equations, the system copies the essential fluid behavior patterns into a lightweight neural network that can be evaluated rapidly. This copy maintains sufficient accuracy for design exploration while dramatically reducing computational burden.

The neural network copies high-fidelity fluid dynamics behavior from expensive physical models and experimental data, preserving accuracy without requiring the computational overhead of traditional approximation methods. The network learns complex nonlinear relationships directly from training data, capturing turbulent flow patterns and separation phenomena that simplified models miss.

The patent changes the parameter representation by using neural network weights and activations to encode fluid state variables instead of solving differential equations. This parameter transformation allows the system to maintain high precision while achieving computational efficiency, as the network evaluates predefined mathematical functions rather than iteratively solving complex PDEs.

The patent substitutes the mechanical system of solving differential equations with a data-driven neural network model. Instead of relying on explicit physical formulations and iterative numerical solvers, the system uses learned representations from training data to predict fluid behavior. This substitution maintains reliability by grounding the network in physical laws during training while reducing computational complexity during inference.

The complex physical modeling knowledge is copied into the neural network architecture through training on high-fidelity simulation data and experimental measurements. The network internalizes complex fluid-structure interaction patterns, boundary layer behaviors, and turbulent flow characteristics, making them accessible through simple forward propagation without requiring the original complex computational infrastructure.