Computational study demonstrates accurate modeling of sharp transitions in multiparameter dynamical systems, indicating effective neural approximation across contrasting physical scales.
Key Points
To extend a two-scale neural network method to resolve singularly perturbed dynamical systems governed by multiple small parameters.
Calculated a single effective scale parameter derived from the geometric mean of all small system parameters.
Augmented the neural network input layer with scale-aware features to intrinsically capture steep gradient transitions.
Tested the framework across coupled dynamical systems with high-contrast, multiparameter configurations.
The augmented neural framework successfully captured sharp solution transitions across multiple interacting scales without requiring fine-tuned spatial meshes.
The geometric-mean scaling preserved high numerical accuracy across coupled dynamical systems characterized by widely contrasting small parameters.