Neural Network Permittivity Imaging via Scattering Simulation

The patent transforms the scattering problem from a physical parameter domain into a neural network parameter domain. By representing the scattering process as a neural network with learnable parameters (node functions and weights), the system can accurately model non-linear multiple scattering effects without requiring complex traditional computational electromagnetics solvers. The neural network parameters are trained to match measured scattering data, enabling accurate permittivity imaging while simplifying the forward modeling process.

The patent replaces traditional mechanical/computational physics-based scattering solvers with a data-driven neural network approach. Instead of solving Maxwell's equations or wave equations numerically to model pulse scattering, the system uses a trained neural network that has learned the scattering behavior from training data. This substitution eliminates the need for complex iterative numerical solvers while accurately capturing non-linear multiple scattering effects.

The patent inverts the conventional neural network parameterization by fixing the node functions (using physics-informed basis functions) and making the connection weights the learnable parameters. This inversion allows the network to efficiently represent non-linear permittivity distributions while maintaining fast convergence during training. The fixed functions encode physical constraints and the variable weights adapt to the specific scattering scenario.

The patent performs preliminary action by pre-defining the neural network node functions with physics-informed basis functions before training. This preliminary setup encodes physical knowledge about scattering and permittivity relationships into the network architecture, so that during training only the weights need to be learned from data. This reduces the dimensionality of the learning problem and accelerates convergence while maintaining accuracy.

The patent creates a computational copy of the physical scattering process in the form of a trained neural network. Instead of directly solving the complex non-linear scattering problem for each imaging task, the system trains a neural network to copy the scattering behavior from training data. Once trained, this computational copy can rapidly predict scattering patterns for any given permittivity distribution, enabling accurate imaging without repeatedly solving complex non-linear equations.

The patent implements self-service by using the neural network to automatically model and compensate for multiple scattering effects during the imaging process. The trained network inherently understands the non-linear scattering physics and can process measured signals to produce accurate permittivity images without requiring manual intervention or complex iterative correction algorithms. The system serves itself by using the same neural network architecture for both forward modeling and inverse imaging.