BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces

Bubbly flows exhibit complex multiscale dynamics, with deformable bubbles interacting through the surrounding liquid and giving rise to strongly coupled kinematic and morphological behavior. We present BubbleSH, a bubbly flows dataset consisting of transient, three-dimensional bubble-swarm dynamics obtained from high-fidelity direct numerical simulations of bubbles rising in a periodic domain. The dataset provides time-resolved bubble trajectories, velocities, and shape evolution, with bubble morphology compactly represented using spherical harmonics. Designed to be lightweight yet physically expressive, the dataset enables data-driven modeling of bubbly flow simulators where shape deformation and bubble-bubble interactions play a central role. We characterize the dataset with bubble kinematics, morphology, and interaction patterns, and introduce evaluation metrics for both trajectory and shape prediction. The sensitivity of bubble-swarm dynamics to local perturbations makes BubbleSH particularly well suited to generative models that learn distributions over possible future trajectories. We evaluate a permutationally and translationally equivariant probabilistic emulator on BubbleSH given the proposed metrics. Therefore, we establish a compact, high-fidelity dataset and a benchmark for developing and evaluating data-driven models of deformable, chaotic multiphase systems.

Deep Operator Networks for Surrogate Modeling of Cyclic Adsorption Processes with Varying Initial Conditions

Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In particular, DeepONets offer a natural formulation for PDE solving, since the solution of a partial differential equation can be interpreted as an operator mapping an initial condition to its corresponding solution field. In this work, we applied DeepONets in the context of process modeling for adsorption technologies, to assess their feasibility as surrogates for cyclic adsorption process simulation and optimization. The goal is to accelerate convergence of cyclic processes such as Temperature-Vacuum Swing Adsorption (TVSA), which require repeated solution of transient PDEs, which are computationally expensive. Since each step of a cyclic adsorption process starts from the final state of the preceding step, effective surrogate modeling requires generalization across a wide range of initial conditions. The governing equations exhibit steep traveling fronts, providing a demanding benchmark for operator learning. To evaluate functional generalization under these conditions, we construct a mixed training dataset composed of heterogeneous initial conditions and train DeepONets to approximate the corresponding solution operators. The trained models are then tested on initial conditions outside the parameter ranges used during training, as well as on completely unseen functional forms. The results demonstrate accurate predictions both within and beyond the training distribution, highlighting DeepONets as potential efficient surrogates for accelerating cyclic adsorption simulations and optimization workflows.