Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows

This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive. To address this, the chapter surveys state-of-the-art SciML methods for building efficient surrogate models, including linear reduced-order techniques based on Singular Value Decomposition (such as Dynamic Mode Decomposition) and nonlinear neural network approaches like Physics-Informed Neural Networks (PINNs) and $β$-Variational Autoencoders ($β$-VAEs). It first covers the authors' work combining these models with High Performance Computing strategies, including Adaptive Mesh Refinement/Coarsening (AMR/C) and scientific floating-point data compression. It then presents two new contributions: surrogate modeling of turbidity currents via PINNs, and the extraction of disentangled nonlinear modes from thermal flows using $β$-VAEs. Governing equations and representative benchmarks, including lock-exchange flows and Rayleigh-Bénard convection, illustrate these methodologies. The chapter is intentionally long, covering both the mathematical and physical foundations of coupled fluid flow and the computational aspects of state-of-the-art modeling. Overall, it demonstrates how SciML enables fast, accurate approximations of complex coupled systems within the specific data regimes and modeling assumptions considered, while substantially reducing computational cost relative to full-order simulations. Broader capabilities such as real-time prediction and uncertainty quantification remain active research directions whose feasibility depends strongly on the problem at hand.

A flow surrogate validated on a simple regime is often taken as evidence that the approach will carry to a richer one. We test this assumption on two transient flows under time-varying boundary conditions emulating the process startup: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), a core semiconductor-manufacturing process, and the two-dimensional Karman vortex street (KVS) behind a cylinder. Eight surrogate models are compared on one shared evaluation pipeline, differing in whether they learn the full field or a latent representation, and whether they predict trajectories in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the process-relevant cumulative wall shear stress to 3.2% relative error. On the wake, a latent autoregressive DeepONet retains 96% of the shedding power that direct and one-shot models damp to almost zero. The deciding axis is the treatment of time. The self-sustained wake requires the phase memory that autoregressive feedback provides, while the boundary-driven film rewards a direct map. Pointwise RMSE picks the wrong model in both regimes, so the evaluation scores five physical questions instead, the field, its structure, invented motion, amplitude, and timing. The trained surrogates answer queries $10^3$ to $10^4$ times faster than the finite-element solver, but the offline cost of the training simulations means they pay off from the first query beyond the training set for CMP and the third for the KVS. The choice of surrogate should follow the dynamical character of the target flow, and its validation should use failure-mode-resolved metrics, since neither the winning architecture nor its validation transfers.

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.