Benchmarking Structural Nonlinearities with Interpretable Deep Learning

Thu, 11 Sep 2025 00:00:00 +0000

By Bayan Abusalameh

TL;DR.

Linear oscillators are simple and elegant: each mode evolves independently, superposition holds, and responses remain fully predictable. Once nonlinearities enter—whether clearance, Coulomb friction, cubic stiffness (hardening or softening), or quadratic damping—the story changes. Resonances shift, signals distort, and energy begins to leak and exchange in unexpected ways.

Our benchmark captures this transition by generating controlled SDOF simulations that span both linear and nonlinear regimes, injecting realistic noise, and labeling each sample automatically. On top of this, we train neural networks and evaluate interpretability maps to reveal not only what the model predicts, but also why.

From Decoupled Linear Modes to Nonlinear Mode Interaction

Mon, 08 Sep 2025 00:00:00 +0000

Why superposition breaks, energy starts to slosh, and what to look for in data

TL;DR. In the linear regime, each mode is an independent damped oscillator—clean, decoupled, and predictable. As amplitudes grow (or when damping/forcing aren’t “nice”), cross terms re-couple the modal equations. Near internal resonance (e.g., 1:1, 2:1, 3:1 ratios), those cross terms become near-resonant drives, and you see energy exchange, sidebands, and new frequencies. That’s “mode interaction.” Our benchmark builds controlled simulations that span both regimes and labels interaction strength automatically.

Research on Bayan Abusalameh

Benchmarking Structural Nonlinearities with Interpretable Deep Learning

From Decoupled Linear Modes to Nonlinear Mode Interaction