FAMIR: Future-aligned latent dynamics for complex-flow forecasting
Abstract
Learned flow surrogates are applied recursively, so errors in phase, amplitude and transport accumulate as each prediction feeds the next. During training, however, the realized next state is known. We propose Future-Aligned Motion Inference for Recursive Physical Forecasting (FAMIR), which uses this realized future to shape the signal that drives the update, not only the predicted state. On the latent grid of a frozen autoencoder, a future-conditioned teacher and a history-only student infer motion tensors that condition one shared residual transition. Posterior--Prior Motion Alignment (PPMA) jointly aligns the teacher (posterior) and student (prior) motions, prediction-fed multistep objectives train the student on its own rollouts, and only the student is deployed. On viscoelastic channel flow, Rayleigh--Bénard convection and planetary shallow-water flow, FAMIR achieves lower complete-prefix normalized root-mean-square error than three direct latent predictors of comparable size and a delay-embedded linear reference at ten steps (1.003\%, 1.055%, 0.620%) and twenty steps (1.661%, 1.683%, 1.036%). Its advantage is largest at the first step in the viscoelastic flow and grows with lead time in the other flows. Over forty-step forecasts, FAMIR keeps fluctuation profiles and probability densities closer to the reference than the direct predictors. Without the teacher, the motion-conditioned student already outperforms the direct predictors; in the shallow-water flow, prediction-fed rollouts are decisive and joint alignment is far more effective than distillation toward a fixed teacher (1.036% against 1.874%). Fixed-state interventions show that the trained update relies on the state-specific motion, and the deployed student matches the one-step accuracy of the future-informed teacher.
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BibTeX
@misc{chen2026famir,
title = {{FAMIR: Future-aligned latent dynamics for complex-flow forecasting}},
author = {Yuxuan Chen and Yan Wang and Haotian Cheng and Hongna Zhang and Wenhua Zhang and Yuke Li and Xiaobin Li and Fengchen Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36515},
eprint = {2610.36515},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36515},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - FAMIR: Future-aligned latent dynamics for complex-flow forecasting
AU - Yuxuan Chen
AU - Yan Wang
AU - Haotian Cheng
AU - Hongna Zhang
AU - Wenhua Zhang
AU - Yuke Li
AU - Xiaobin Li
AU - Fengchen Li
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36515
UR - https://arxiv.org/abs/2610.36515
AB - Learned flow surrogates are applied recursively, so errors in phase, amplitude and transport accumulate as each prediction feeds the next. During training, however, the realized next state is known. We propose Future-Aligned Motion Inference for Recursive Physical Forecasting (FAMIR), which uses this realized future to shape the signal that drives the update, not only the predicted state. On the latent grid of a frozen autoencoder, a future-conditioned teacher and a history-only student infer motion tensors that condition one shared residual transition. Posterior--Prior Motion Alignment (PPMA) jointly aligns the teacher (posterior) and student (prior) motions, prediction-fed multistep objectives train the student on its own rollouts, and only the student is deployed. On viscoelastic channel flow, Rayleigh--Bénard convection and planetary shallow-water flow, FAMIR achieves lower complete-prefix normalized root-mean-square error than three direct latent predictors of comparable size and a delay-embedded linear reference at ten steps (1.003\%, 1.055%, 0.620%) and twenty steps (1.661%, 1.683%, 1.036%). Its advantage is largest at the first step in the viscoelastic flow and grows with lead time in the other flows. Over forty-step forecasts, FAMIR keeps fluctuation profiles and probability densities closer to the reference than the direct predictors. Without the teacher, the motion-conditioned student already outperforms the direct predictors; in the shallow-water flow, prediction-fed rollouts are decisive and joint alignment is far more effective than distillation toward a fixed teacher (1.036% against 1.874%). Fixed-state interventions show that the trained update relies on the state-specific motion, and the deployed student matches the one-step accuracy of the future-informed teacher.
ER -