# Interactive 4D Volumetric Liquid Forecasting under Moving-Solid Interaction

arXiv: https://arxiv.org/abs/2610.16167 · HTML: https://mlsanity.com/paper/2610.16167/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 27 of 27)

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- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
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- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
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- [Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains](https://mlsanity.com/paper/2505.18781/) (2025)
- [APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs](https://mlsanity.com/paper/2411.00180/) (2024)
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- [4DFlowNet: Super-Resolution 4D Flow MRI using Deep Learning and Computational Fluid Dynamics](https://mlsanity.com/paper/2004.07035/) (2020)
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- [InterDyn: Controllable Interactive Dynamics with Video Diffusion Models](https://mlsanity.com/paper/2412.11785/) (2024)
- [Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs](https://mlsanity.com/paper/2602.02788/) (2026)
- [Physics-informed graph neural networks for flow field estimation in carotid arteries](https://mlsanity.com/paper/2408.07110/) (2024)
- [Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs](https://mlsanity.com/paper/2505.17575/) (2025)
- [3D Neural Operator-Based Flow Surrogates around 3D geometries: Signed Distance Functions and Derivative Constraints](https://mlsanity.com/paper/2503.17289/) (2025)
- [Learning an Implicit Physics Model for Image-based Fluid Simulation](https://mlsanity.com/paper/2508.08254/) (2025)
- [Neural Latent Arbitrary Lagrangian-Eulerian Grids for Fluid-Solid Interaction](https://mlsanity.com/paper/2603.00792/) (2026)
- [A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structures](https://mlsanity.com/paper/2503.22252/) (2025)
- [NeurIPS 2024 ML4CFD Competition: Results and Retrospective Analysis](https://mlsanity.com/paper/2506.08516/) (2025)
- [Learning Particle Dynamics Subject to Rigid Body Manipulations Using Graph Neural Networks](https://mlsanity.com/paper/2509.03446/) (2025)

## Abstract (arXiv)

We propose the task of Interactive 4D Volumetric Liquid Forecasting: predicting the spatiotemporal evolution of a future dense 3D liquid velocity field conditioned on how a solid object moves through it. This task provides an upstream physical forecasting primitive for systems that need to reason about motion-conditioned liquid response, including robotic liquid manipulation, digital twins, and rigid-fluid video generation. Existing works have made efforts in predicting flow around static or prescribed solid geometries and synthesizing visually plausible fluid motion. Yet these approaches provide limited coverage for interactive liquid dynamics, as they are not capable of forecasting how a moving solid induces a future full-domain liquid response. In this forecasting scenario, the hydrodynamic effect is condensed near an evolving liquid-solid interface, but the prediction target is a global spatiotemporal rollout. To address this challenge, we propose a two-level recurrent forecasting framework, TIDE/TIDES: TIDE isolates localized interface-driven forecasting, while TIDES adds transport-aware coupling and explicit stabilization to reduce accumulated rollout error. Across adapted neighboring baselines, controlled component ablations, motion/size OOD tests, and long-horizon evaluation, TIDES achieves the best forecasting performance and the ablations identify localized interaction, transport coupling, and stabilization as the key contributors. Together, our task formulation, benchmark, and TIDE/TIDES study establish a controlled foundation for moving-solid-conditioned dense liquid forecasting. The code is publicly available at https://github.com/jongwonryu/TIDE-TIDES.