Fast Probabilistic Material Characterization: Amortized Simulation-Based Inference for Phenomenological Models

Abstract

The calibration of phenomenological constitutive models for heterogeneous materials, such as recycled thermoplastics, remains fundamentally bottlenecked by the prohibitive computational cost of iterative finite element model updating. Furthermore, traditional point-estimate calibrations discard crucial uncertainty stemming from intra-lot scatter, model discrepancy, and measurement noise. To overcome these limitations, we formulate material calibration as a hierarchical stochastic inverse problem and solve it using amortized simulation-based inference via neural posterior estimation. By integrating a fast numerical surrogate into a hierarchical data wrapper, we learn a global conditional posterior that maps multi-coupon experimental responses directly to latent material parameters in a single forward pass. This amortized approach collapses the nested loops that conventionally preclude material-driven design: it eliminates the inner loop of iterative finite-element model updating or Markov-chain Monte Carlo sampling, thereby freeing the outer loop of blend and ratio exploration. The result is the near-instantaneous, uncertainty-aware estimation of phenomenological parameters and their intra-lot spread, extracted from repeated coupon measurements via a single neural forward pass. We demonstrate this architecture on uniaxial tensile data from post-consumer polypropylene blends. While comprehensive characterization ultimately requires multiaxial testing, capturing this intrinsic variance establishes the foundation required for robust design under uncertainty, accelerating the qualification of variable recyclates for circular economy workflows.