# Model-Agnostic AI Framework with Explicit Time Integration for Long-Term Fluid Dynamics Prediction

arXiv: https://arxiv.org/abs/2412.05657 · HTML: https://mlsanity.com/paper/2412.05657/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 7 Dec 2024.

## Builds on (most cited first, 16 of 16)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics](https://mlsanity.com/paper/2205.03990/) (2022)
- [Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation](https://mlsanity.com/paper/2311.07896/) (2023)
- [Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamics](https://mlsanity.com/paper/2402.12971/) (2024)
- [Graph Convolutional Neural Networks for Body Force Prediction](https://mlsanity.com/paper/2012.02232/) (2020)
- [Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator](https://mlsanity.com/paper/2206.07680/) (2022)
- [Residual-based physics-informed transfer learning: A hybrid method for accelerating long-term CFD simulations via deep learning](https://mlsanity.com/paper/2206.06817/) (2022)
- [Strategies for Pretraining Neural Operators](https://mlsanity.com/paper/2406.08473/) (2024)
- [Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flows](https://mlsanity.com/paper/2105.03332/) (2021)
- [Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective](https://mlsanity.com/paper/2401.08667/) (2024)
- [Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Prediction](https://mlsanity.com/paper/2406.03789/) (2024)

## Built on by (most cited first, 3 of 3)

- [Rigid-Deformation Decomposition AI Framework for 3D Spatio-Temporal Prediction of Vehicle Collision Dynamics](https://mlsanity.com/paper/2503.19712/) (2025)
- [Spatio-Temporal Forecasting of Retaining Wall Deformation: Mitigating Error Accumulation via Multi-Resolution ConvLSTM Stacking Ensemble](https://mlsanity.com/paper/2603.10453/) (2026)
- [The balance between compactness and forecast accuracy of data-driven latent-space reduced-order models in controlled wake flows](https://mlsanity.com/paper/2607.24569/) (2026)

## Abstract (arXiv)

This study addresses the critical challenge of error accumulation in spatio-temporal auto-regressive (AR) predictions within scientific machine learning models by exploring temporal integration schemes and adaptive multi-step rollout strategies. We introduce the first implementation of the two-step Adams-Bashforth method specifically tailored for data-driven AR prediction, leveraging historical derivative information to enhance numerical stability without additional computational overhead. To validate our approach, we systematically evaluate time integration schemes across canonical 2D PDEs before extending to complex Navier-Stokes cylinder vortex shedding dynamics. Additionally, we develop three novel adaptive weighting strategies that dynamically adjust the importance of different future time steps during multi-step rollout training. Our analysis reveals that as physical complexity increases, such sophisticated rollout techniques become essential, with the Adams-Bashforth scheme demonstrating consistent robustness across investigated systems and our best adaptive approach delivering an 89% improvement over conventional fixed-weight methods while maintaining similar computational costs. For the complex Navier-Stokes vortex shedding problem, despite using an extremely lightweight graph neural network with just 1,177 trainable parameters and training on only 50 snapshots, our framework accurately predicts 350 future time steps reducing mean squared error from 0.125 (single-step direct prediction) to 0.002 (Adams-Bashforth with proposed multi-step rollout). Our integrated methodology demonstrates an 83% improvement over standard noise injection techniques and maintains robustness under severe spatial constraints; specifically, when trained on only a partial spatial domain, it still achieves 58% and 27% improvements over direct prediction and forward Euler methods, respectively.