Wenxiao Pan

Zhan Ma, Zisheng Ye, Wenxiao Pan

Predicting the dynamic behaviors of particles in suspension subject to hydrodynamic interaction (HI) and external drive can be critical for many applications. By harvesting advanced deep learning techniques, the present work introduces a new framework, hydrodynamic interaction graph neural network (HIGNN), for inferring and predicting the particles' dynamics in Stokes suspensions. It overcomes the limitations of traditional approaches in computational efficiency, accuracy, and/or transferability. In particular, by uniting the data structure represented by a graph and the neural networks with learnable parameters, the HIGNN constructs surrogate modeling for the mobility tensor of particles which is the key to predicting the dynamics of particles subject to HI and external forces. To account for the many-body nature of HI, we generalize the state-of-the-art GNN by introducing higher-order connectivity into the graph and the corresponding convolutional operation. For training the HIGNN, we only need the data for a small number of particles in the domain of interest, and hence the training cost can be maintained low. Once constructed, the HIGNN permits fast predictions of the particles' velocities and is transferable to suspensions of different numbers/concentrations of particles in the same domain and to any external forcing. It has the ability to accurately capture both the long-range HI and short-range lubrication effects. We demonstrate the accuracy, efficiency, and transferability of the proposed HIGNN framework in a variety of systems. The requirement on computing resource is minimum: most simulations only require a desktop with one GPU; the simulations for a large suspension of 100,000 particles call for up to 6 GPUs.

Pouria Behnoudfar, Deekshith Naidu Ponnana, Noah J. Schmelzer et al.

We present a probabilistic modeling framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials. Spatially heterogeneous material state fields are represented using probability density functions (PDFs), providing a principled statistical description of microstructural variability and state evolution across different computational polycrystalline realizations. The framework is built on the inverse identification of a probabilistic transport model, formulated as a Liouville equation with an unknown drift term. To enable accurate, stable, and interpretable inference of this drift field in high-dimensional, transport-dominated settings, we develop a Separable Probability Learning Technique via Physics-Informed Neural Networks (SPLIT-PINN). This method incorporates a marginal-correction drift decomposition, orthogonality constraints, and residual-based adaptive training to enhance well-posedness, numerical stability, and physical consistency without imposing restrictive parametric assumptions. Using SPLIT-PINN, the drift field governing the temporal evolution of joint state PDFs is inferred directly from data. After benchmark validation, the framework is applied to physical computational datasets describing the evolution of polycrystalline microstructural states, including von Mises stress, dislocation density, and equivalent plastic strain rate. The learned Liouville model, trained on a single dataset, is subsequently used in forward predictions of the temporal evolution of joint and marginal PDFs for multiple unseen polycrystal realizations. Quantitative comparisons with reference PDFs demonstrate that the proposed framework yields accurate and robust probabilistic predictions and generalizes effectively across datasets.