Data-Driven Nonlinear Modal Analysis: A Deep Learning Approach

We present a data-driven method based on deep learning for identifying nonlinear normal modes of unknown nonlinear dynamical systems using response data only. We leverage the modeling capacity of deep neural networks to identify the forward and inverse nonlinear modal transformations and the associated modal dynamics evolution. We test the method on Duffing systems with cubic nonlinearity and observe that the identified NNMs with invariant manifolds from response data agree with those analytical or numerical ones using closed-form equations.