Improving Long-term Autoregressive Spatiotemporal Predictions: A Proof of Concept with Fluid Dynamics

• URL: http://arxiv.org/abs/2508.18565v1
• Date: Mon, 25 Aug 2025 23:51:18 GMT
• Title: Improving Long-term Autoregressive Spatiotemporal Predictions: A Proof of Concept with Fluid Dynamics
• Authors: Hao Zhou, Sibo Cheng,
• Abstract summary: For complex systems, long-term accuracy often deteriorates due to error accumulation.<n>We propose the PushForward framework, which retains one-step-ahead training while enabling multi-step learning.<n> SPF builds a supplementary dataset from model predictions and combines it with ground truth via an acquisition strategy.
• Score: 10.71350538032054
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Data-driven methods are emerging as efficient alternatives to traditional numerical forecasting, offering fast inference and lower computational cost. Yet, for complex systems, long-term accuracy often deteriorates due to error accumulation, and autoregressive training (though effective) demands large GPU memory and may sacrifice short-term performance. We propose the Stochastic PushForward (SPF) framework, which retains one-step-ahead training while enabling multi-step learning. SPF builds a supplementary dataset from model predictions and combines it with ground truth via a stochastic acquisition strategy, balancing short- and long-term performance while reducing overfitting. Multi-step predictions are precomputed between epochs, keeping memory usage stable without storing full unrolled sequences. Experiments on the Burgers' equation and the Shallow Water benchmark show that SPF achieves higher long-term accuracy than autoregressive methods while lowering memory requirements, making it promising for resource-limited and complex simulations.

Related papers

• TARFVAE: Efficient One-Step Generative Time Series Forecasting via TARFLOW based VAE [3.7770105485163206]
  This paper presents TARFVAE, a novel generative framework that combines the Transformer-based autoregressive flow (TARFLOW) and variational autoencoder (VAE) for efficient one-step generative time series forecasting.<n>With simple modules, TARFVAE achieves superior performance over state-of-the-art deterministic and generative models across different forecast horizons on datasets.
  arXiv  Detail & Related papers  (2025-11-28T03:19:14Z)
• PPMStereo: Pick-and-Play Memory Construction for Consistent Dynamic Stereo Matching [51.98089287914147]
  textbfPick-and-textbflay textbfMemory (PM) construction module for dynamic bfStereo matching, dubbed as bftextPPMStereo.<n>Inspired by the two-stage decision-making process in humans, we propose a textbfPick-and-textbflay textbfMemory (PM) construction module for dynamic bfStereo matching, dubbed as bftextPPMStereo.
  arXiv  Detail & Related papers  (2025-10-23T03:52:39Z)
• Online Kernel Dynamic Mode Decomposition for Streaming Time Series Forecasting with Adaptive Windowing [3.6194446038160315]
  We introduce WORK-DMD (Windowed Online Random Kernel Dynamic Mode Decomposition), a method that combines Random Fourier Features with online Dynamic Mode Decomposition to capture nonlinear dynamics.<n> WORK-DMD employs Sherman-Morrison updates within rolling windows, enabling continuous adaptation to evolving dynamics from only current data.<n> Experiments on benchmark datasets across several domains show that WORK-DMD achieves higher accuracy than several state-of-the-art online forecasting methods.
  arXiv  Detail & Related papers  (2025-10-17T07:57:37Z)
• Inference-Time Scaling of Diffusion Language Models with Particle Gibbs Sampling [70.8832906871441]
  We study how to steer generation toward desired rewards without retraining the models.<n>Prior methods typically resample or filter within a single denoising trajectory, optimizing rewards step-by-step without trajectory-level refinement.<n>We introduce particle Gibbs sampling for diffusion language models (PG-DLM), a novel inference-time algorithm enabling trajectory-level refinement while preserving generation perplexity.
  arXiv  Detail & Related papers  (2025-07-11T08:00:47Z)
• Enhanced accuracy through ensembling of randomly initialized auto-regressive models for time-dependent PDEs [0.0]
  Autoregressive inference with machine learning models suffer from error accumulation over successive predictions, limiting their long-term accuracy.<n>We propose a deep ensemble framework to address this challenge, where multiple ML surrogate models are trained in parallel and aggregated during inference.<n>We validate the framework on three PDE-driven dynamical systems - stress evolution in heterogeneous microstructures, Gray-Scott reaction-diffusion, and planetary-scale shallow water system.
  arXiv  Detail & Related papers  (2025-07-05T02:25:12Z)
• Accelerated Test-Time Scaling with Model-Free Speculative Sampling [58.69141724095398]
  We introduce STAND (STochastic Adaptive N-gram Drafting), a novel model-free speculative decoding approach.<n>We show that STAND reduces inference latency by 60-65% compared to standard autoregressive decoding.<n>As a model-free approach, STAND can be applied to any existing language model without additional training.
  arXiv  Detail & Related papers  (2025-06-05T07:31:18Z)
• An Adaptive Framework for Autoregressive Forecasting in CFD Using Hybrid Modal Decomposition and Deep Learning [3.1337872355726084]
  This work presents, to the best of the authors' knowledge, the first generalizable and fully data-driven adaptive framework designed to stabilize deep learning (DL) autoregressive forecasting models over long time horizons.<n>The proposed methodology alternates between two phases: (i) predicting the evolution of the flow field over a selected time interval using a trained DL model, and (ii) updating the model with newly generated CFD data when stability degrades, thus maintaining accurate long-term forecasting.<n>The framework is validated across three increasingly complex flow regimes, from laminar to turbulent, demonstrating from 30 % to 95
  arXiv  Detail & Related papers  (2025-05-02T18:33:41Z)
• MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation [48.41289705783405]
  We propose a PDE-embedded network with multiscale time stepping (MultiPDENet)<n>In particular, we design a convolutional filter based on the structure of finite difference with a small number of parameters to optimize.<n>A Physics Block with a 4th-order Runge-Kutta integrator at the fine time scale is established that embeds the structure of PDEs to guide the prediction.
  arXiv  Detail & Related papers  (2025-01-27T12:15:51Z)
• Federated Smoothing Proximal Gradient for Quantile Regression with Non-Convex Penalties [3.269165283595478]
  Distributed sensors in the internet-of-things (IoT) generate vast amounts of sparse data. We propose a federated smoothing proximal gradient (G) algorithm that integrates a smoothing mechanism with the view, thereby both precision and computational speed.
  arXiv  Detail & Related papers  (2024-08-10T21:50:19Z)
• Deep Ensembles Meets Quantile Regression: Uncertainty-aware Imputation for Time Series [45.76310830281876]
  We propose Quantile Sub-Ensembles, a novel method to estimate uncertainty with ensemble of quantile-regression-based task networks. Our method not only produces accurate imputations that is robust to high missing rates, but also is computationally efficient due to the fast training of its non-generative model.
  arXiv  Detail & Related papers  (2023-12-03T05:52:30Z)
• Deep Equilibrium Optical Flow Estimation [80.80992684796566]
  Recent state-of-the-art (SOTA) optical flow models use finite-step recurrent update operations to emulate traditional algorithms. These RNNs impose large computation and memory overheads, and are not directly trained to model such stable estimation. We propose deep equilibrium (DEQ) flow estimators, an approach that directly solves for the flow as the infinite-level fixed point of an implicit layer.
  arXiv  Detail & Related papers  (2022-04-18T17:53:44Z)
• Learning representations with end-to-end models for improved remaining useful life prognostics [64.80885001058572]
  The remaining Useful Life (RUL) of equipment is defined as the duration between the current time and its failure. We propose an end-to-end deep learning model based on multi-layer perceptron and long short-term memory layers (LSTM) to predict the RUL. We will discuss how the proposed end-to-end model is able to achieve such good results and compare it to other deep learning and state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-04-11T16:45:18Z)
• Extrapolation for Large-batch Training in Deep Learning [72.61259487233214]
  We show that a host of variations can be covered in a unified framework that we propose. We prove the convergence of this novel scheme and rigorously evaluate its empirical performance on ResNet, LSTM, and Transformer.
  arXiv  Detail & Related papers  (2020-06-10T08:22:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.