Nonlinear oscillators are ubiquitous in physics and engineering, yet finding explicit analytical expressions for their amplitude-dependent frequency remains a fundamental challenge. The Duffing equation is the paradigmatic model for this class of problems, and despite decades of progress through perturbative, variational, and homotopic methods, general closed-form frequency relations are unavailable for most of its configurations. In this work, we investigate whether symbolic regression (SR)—a machine-learning technique that searches for interpretable mathematical expressions directly from data—can recover the closed-form amplitude-frequency relations produced by classical methods, and approximate them where no closed form is available. We generate reference datasets using four classical approaches: the Lindstedt-Poincaré method, first-harmonic balance, multiharmonic balance, and numerical integration via a Runge-Kutta 4–5 scheme. We stress at the outset that, for the analytical and semianalytical methods, the training labels are obtained by evaluating the corresponding closed-form expressions; recovering those expressions therefore constitutes symbolic rediscovery of a known formula from sampled data, rather than discovery of new physics. The only genuinely dynamics-based case is the quintic oscillator labeled with Runge-Kutta integration followed by spectral analysis. SR, implemented through PySR, is then trained on these datasets for six configurations spanning cubic, quartic, and quintic nonlinearities under both free and forced conditions. In all free-oscillator datasets the oscillation amplitude is fixed (normalized to $A=1$), so the learned relations are parameter-frequency relations at fixed amplitude. For free oscillators with known analytical solutions, SR reproduces the reference expressions to machine-level numerical precision ($R^2=1.0000$, mean squared error (MSE) $\sim {10}^{-17}$), returning the Lindstedt-Poincaré, harmonic-balance, and first-harmonic-balance expressions used to generate the labels. For forced oscillators, where the response amplitude is defined implicitly as the root of a cubic (or quintic) polynomial in $A^2$, SR captures the dominant resonance structure but cannot fully resolve the implicit-root behavior with the present algebraic operator set ($0.53\le R^2\le 0.83$). These results position SR as a practical complement to classical analytical approaches to nonlinear dynamics, with particular value in contexts where specialized perturbative methods are inaccessible or their validity is restricted to narrow parameter regimes. We are explicit about the limits of the present scope: amplitude dependence, robustness to noise, extrapolation beyond the training box, and run-to-run variability of the stochastic search are identified as the validation steps required before any claim of genuine discovery can be made.

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• Chaos
• Classical mechanics
• Nonlinear waves
• Chaos & nonlinear dynamics
• Machine learning