Prediction of Viscoelastic Droplet Impact Dynamics Using a Vision Transformer-Based Approach

Void fraction, which quantifies the proportion of the fluid flow volume occupied by the gas phase, is a key parameter in the characterization of gas-liquid two-phase flow. Existing estimation methods either rely on flow assumptions that do not generalize across different fluids or on intrusive sensing that disturbs the flow behavior. We propose VFNet, a dual-branch spatio-temporal neural network for void-fraction prediction from synchronized multi-view videos of two-phase flow. A local branch extracts features from confined spatial regions and fuses the synchronized dual views, while a spatio-temporal branch captures the global evolution of the flow across space and time to refine a coarse geometric estimate. Trained on simulated computational fluid dynamics (CFD) data with known ground-truth void fractions and evaluated against both learning-based and traditional baselines, VFNet achieves the best performance across a broad range of metrics and also improves downstream flow-pattern classification on real two-phase flow data.

Spreading of liquid droplets on solid substrates constitutes a classic multiphysics problem with widespread applications ranging from inkjet printing, spray cooling, to biomedical microfluidic systems. Yet, accurate computational fluid dynamic (CFD) simulations are prohibitively expensive, taking more than 18 to 24 hours for each transient computation. In this paper, Physics-Informed Laplace Operator Neural Network (PI-LNO) is introduced, representing a novel architecture where the Laplace integral transform function serves as a learned physics-informed functional basis. Extensive comparative benchmark studies were performed against five other state-of-the-art approaches: UNet, UNet with attention modules (UNet-AM), DeepONet, Physics-Informed UNet (PI-UNet), and Laplace Neural Operator (LNO). Through complex Laplace transforms, PI-LNO natively models the exponential transient dynamics of the spreading process. A TensorFlow-based PI-LNO is trained on multi-surface CFD data spanning contact angles $θ_s ε[20,160]$, employing a physics-regularized composite loss combining data fidelity (MSE, MAE, RMSE) with Navier-Stokes, Cahn-Hilliard, and causality constraints.

Fast prediction of the response of adhesive soft viscoelastic contacts represents a current challenge in soft robotics and for gripping and manipulation tasks. Determining the complete time-resolved force trajectory requires full numerical simulations, whose computational cost is strongly parameter-dependent, making them impractical for real-time application or design-optimization loops. In this work, we overcome this limitation by training a scalar-conditioned, stateful, sequence-to-sequence deep learning model to predict the full force evolution from a prescribed displacement history for both short- and long-range adhesion regimes. The data set spans four orders of magnitude in loading and unloading rates and includes varied dwell times, with the Tabor parameter ranging from $0.2$ to $3.2$. To enable learning across these heterogeneous time scales, we introduce a fixed-measurement-step (FMS) representation that converts variable-length trajectories into fixed-length sequences while preserving their physical-time information. Different architectures were trained, including long short-term memory (LSTM) networks, temporal convolutional neural (TCN) networks, and time-distributed dense layers with three different Tabor-conditioning mechanisms. The models were compared using global waveform and error metrics. We found that the best-performing model has an LSTM architecture with concatenated conditioning, which achieves a held-out mean-squared error of $5.0\times10^{-4}$, a median pull-off-force error of $\approx2.2\%$, and a median hysteresis error of $\approx1.1\%$. For the held-out protocols, the model predicts a complete force trajectory with a median inference time of $0.16$ s. The model is tested across unseen parameter combinations and against analytical limiting cases, providing a rapid surrogate for repeated numerical evaluations with potential use in control-oriented applications.