Transformer-Based Inverse Microrheology for Experimental Mechanics at Ultra-High Strain Rates

Technical Summary: Transformer-Based Inverse Microrheology for Experimental Mechanics at Ultra-High Strain Rates

Problem Statement
Characterizing the rheological properties of soft materials under ultra-high strain rates ($>10^3 \text{ s}^{-1}$) is critical for applications ranging from laser and ultrasound surgery to understanding tissue mechanics. Traditional rheological tools (e.g., oscillatory shear plate rheometry, dynamic mechanical analysis) are limited by spatiotemporal resolution and invasiveness in these extreme regimes. While Inertial Microcavitation Rheometry (IMR) has emerged as a powerful technique to probe nonlinear viscoelastic properties via laser-induced cavitation, its practical application is hindered by computational bottlenecks. Conventional IMR relies on iterative inverse fitting procedures to match experimental bubble dynamics with theoretical models. This process is computationally expensive, limiting scalability and preventing real-time or high-throughput material characterization.

Methodology
The authors introduce the Bubble Dynamics Transformer (BDT), an AI-enhanced experimental mechanics framework designed to bypass iterative optimization. The methodology integrates physics-based simulations with Transformer neural network architectures to perform direct inverse characterization.

1. Experimental Setup: The study utilizes Laser-Induced Cavitation (LIC) within soft materials (PAAm-alginate double-network hydrogels and PEG 8000 solutions). A pulsed laser generates a microbubble, and its radial expansion and collapse ($R(t)$) are recorded using ultra-high-speed imaging (1–10 million fps).
2. Theoretical Modeling: The bubble dynamics are governed by a modified Keller–Miksis equation, treating the surrounding material as a hyper-viscoelastic, incompressible medium. The study employs a Neo-Hookean Kelvin-Voigt (NHKV) constitutive model, where the stress field is defined by a shear modulus ($G$) and a viscosity coefficient ($\mu$).
3. BDT Architecture: The core of the framework is a Transformer-based deep learning model.
   • Input: Time-resolved bubble radius curves ($R(t)$), discretized into 100 data points over a 100 $\mu$s interval.
   • Processing: The model utilizes self-attention mechanisms to capture long-range temporal dependencies in the bubble's transient response (collapse, rebound, and damping). It employs tokenization, positional encoding, multi-head self-attention, and global average pooling.
   • Output: Direct prediction of constitutive parameters ($G$ and $\mu$) without iterative solving.
4. Training Strategy: The BDT models (BDT-Viscoelasticity for $G$ and $\mu$; BDT-ViscousOnly for $\mu$) were trained on synthetic datasets generated from the NHKV-based numerical simulations. The training data spanned logarithmic distributions of shear modulus ($10^3$–$10^6$ Pa) and viscosity ($10^{-4}$–$10^0$ Pa·s), covering a wide range of soft material behaviors.

Key Results

• Inference Accuracy: The BDT models demonstrated high accuracy on synthetic test sets, achieving coefficients of determination ($R^2$) of 0.9981 for shear modulus and 0.9912 for viscosity in the viscoelastic model, and 0.9836 for viscosity in the viscous-only model.
• Experimental Validation:
  • Hydrogels: Applied to PAAm-alginate hydrogels, the BDT-Viscoelasticity model showed excellent agreement with conventional IMR fits for alginate concentrations up to 1.0%. For higher concentrations (1.3% and 2.0%), discrepancies increased (up to ~137% error in $G$), attributed to the emergence of nonlinear stiffening, damage, or network rearrangement mechanisms not captured by the NHKV training model.
  • Viscous Liquids: The BDT-ViscousOnly model successfully inferred effective viscosity for PEG 8000/water mixtures (10–50 w/v%), reproducing the primary collapse and damping features of the experimental dynamics.
• Computational Efficiency: The framework drastically reduces inference time. While synthetic dataset generation took approximately two weeks, the trained models perform inference in roughly 0.6 to 0.7 seconds per sample. This contrasts sharply with the iterative fitting required by conventional IMR, enabling near-real-time characterization.
• Rate-Dependent Behavior: Comparisons with low-frequency rheometer data confirmed significant rate-dependent stiffening in the hydrogels, with LIC-inferred moduli being substantially higher than low-frequency benchmarks.

Significance and Claims
The paper claims that the BDT framework establishes a new, data-driven, and physics-informed route for the rapid inverse characterization of soft materials under extreme loading conditions. By integrating Transformer architectures with physics-based simulations, the work addresses the scalability limitations of traditional IMR, offering a pathway toward high-throughput material screening and intelligent constitutive modeling.

The authors modestly note that the current framework's accuracy is contingent on the target material's response conforming to the NHKV constitutive assumptions used in the synthetic training data. For materials exhibiting complex behaviors such as fracture, plasticity, or heterogeneous dissipation not represented in the training set, accuracy may diminish. Consequently, the authors identify future work as the incorporation of broader constitutive descriptions and richer dissipative physics to improve generalizability. The framework is made publicly available via Hugging Face Spaces and GitHub to support reproducibility and community adoption.