Internal Seminar Series — MathExLab

Interpretable AI for Nonlinear Structural Dynamics and a Benchmark for Nonlinear Mode Interaction

In this internal seminar, I presented my ongoing research on interpretable AI for nonlinear structural dynamics and benchmark design for nonlinear mode interaction.

Seminar Details

Abstract

I introduced a large controlled dataset for detecting nonlinearities in vibrating structures directly from raw time-series signals, together with a post-hoc interpretability pipeline based on Integrated Gradients, DeepLIFT, GradientSHAP, and DeepSHAP, as well as new quantitative metrics for testing attribution fidelity.

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.

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.

A Long Overdue Post

This summer, I had the incredible opportunity to participate in the NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI) Summer School and Workshop at Harvard University — an experience that was as intense as it was inspiring.

Summer School

The summer school (August 4–8, 2025) was a deep dive into cutting-edge topics at the intersection of AI and physics, with lectures from world-class researchers:

Honoured and Inspired: Meeting the Next Generation of STEM Trailblazers

During my trip to Palestine in May 2025, a few remarkable students reached out to ask if I would be willing to give some talks. What followed became one of the most rewarding and energizing experiences of my professional life.

Over just a few days, I had the absolute honour — and joy — of meeting some of the most inspiring young minds I’ve encountered. From brilliant scientists to future engineers, from passionate high schoolers to rising academic leaders, the experience left me both humbled and filled with hope.