Jinkyo Han

Jinkyo Han, Payam Poorsolhjouy, Bahador Bahmani

Micromechanics-based granular models are widely used to predict the failure behavior of porous and particulate materials, including concrete, soils, foams, and biological tissues. Although these models offer considerable flexibility through microstructural parametrization and statistical representation, their mapping to macroscopic responses, particularly failure envelopes, is implicit and requires costly nonlinear, non-smooth simulations, where each failure point is obtained by following a loading trajectory. This limitation is further amplified in inverse settings, where one seeks microstructure configurations that reproduce a target failure response. In this work, we propose a differentiable neural operator that learns the mapping from microstructure configurations to failure envelopes, enabling efficient forward prediction and inverse identification without repeated micromechanical simulations. To ensure mechanical admissibility, we incorporate a physics-informed training strategy that enforces convexity of the predicted envelopes, consistent with Drucker's postulate, thereby eliminating potential non-physical artifacts. We also compare finite difference and automatic differentiation for evaluating the proposed regularization, and find that finite difference provides a favorable practical trade-off in the present DeepONet-based setting. The operator is trained on failure envelopes represented as irregular point clouds, allowing learning from data sampled at heterogeneous resolutions. To further reduce computational cost, we introduce an active learning strategy that adaptively queries the micromechanical model in regions of high epistemic uncertainty. This leads to efficient exploration of the parameter space with fewer high-fidelity simulations. The versatility and performance of the method are demonstrated and benchmarked through several numerical examples.

Jinkyo Han, Bahador Bahmani

Many scientific and engineering systems exhibit intrinsically multimodal behavior arising from latent regime switching and non-unique physical mechanisms. In such settings, learning the full conditional distribution of admissible outcomes in a physically consistent and interpretable manner remains a challenge. While recent advances in machine learning have enabled powerful multimodal generative modeling, their integration with physics-constrained scientific modeling remains nontrivial, particularly when physical structure must be preserved or data are limited. This work develops a physics-informed multimodal conditional modeling framework based on mixture density representations. Mixture density networks (MDNs) provide an explicit and interpretable parameterization of multimodal conditional distributions. Physical knowledge is embedded through component-specific regularization terms that penalize violations of governing equations or physical laws. This formulation naturally accommodates non-uniqueness and stochasticity while remaining computationally efficient and amenable to conditioning on contextual inputs. The proposed framework is evaluated across a range of scientific problems in which multimodality arises from intrinsic physical mechanisms rather than observational noise, including bifurcation phenomena in nonlinear dynamical systems, stochastic partial differential equations, and atomistic-scale shock dynamics. In addition, the proposed method is compared with a conditional flow matching (CFM) model, a representative state-of-the-art generative modeling approach, demonstrating that MDNs can achieve competitive performance while offering a simpler and more interpretable formulation.