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The paper proposes Align Latent Rollout (ALR), a training regularizer that makes neural PDE solvers produce consistent predictions for the same target time regardless of which earlier state the rollout started from. It works by aligning internal representations, so it can be added to existing neural-operator backbones without architectural changes, and the reported gains are better accuracy and lower cross-origin discrepancy on several benchmarks. For ML readers, the main question is whether the gains hold up on harder, longer-horizon, or out-of-distribution settings, since the abstract does not address those.
Same Target, Different Origins: Aligning Latent Rollout for Consistent PDE Emulation
arXiv:2610.21370v1 Announce Type: new Abstract: Neural PDE solvers commonly generate multi-step predictions through autoregressive rollout, recursively applying a learned evolution operator and feeding each prediction back as input for the next step. Approximation errors can therefore propagate through the rollout, causing predictions at a shared target time to depend on their temporal origins and rollout depths. For a well-posed deterministic PDE flow, however, states at different times along the same physical trajectory should, under exact evolution, reach the same target state. To this end, we propose Align Latent Rollout (ALR), a regularization approach that promotes consistency across rollout origins through the neural PDE solver's internal representations. A second-order Taylor analysis of latent discrepancy propagation motivates two objectives: zeroth-order latent state consistency, which aligns representations at a shared target time, and first-order latent dynamics consistency, which aligns local evolution responses to shared perturbations. ALR can be integrated into different neural PDE solvers by regularizing suitable internal representations, without modifying their backbone architectures. Experiments across multiple PDE benchmarks and neural-operator backbones show that ALR improves prediction accuracy while reducing shared-target discrepancies across rollout origins.
Abstract:Neural PDE solvers commonly generate multi-step predictions through autoregressive rollout, recursively applying a learned evolution operator and feeding each prediction back as input for the next step. Approximation errors can therefore propagate through the rollout, causing predictions at a shared target time to depend on their temporal origins and rollout depths. For a well-posed deterministic PDE flow, however, states at different times along the same physical trajectory should, under exact evolution, reach the same target state. To this end, we propose Align Latent Rollout (ALR), a regularization approach that promotes consistency across rollout origins through the neural PDE solver's internal representations. A second-order Taylor analysis of latent discrepancy propagation motivates two objectives: zeroth-order latent state consistency, which aligns representations at a shared target time, and first-order latent dynamics consistency, which aligns local evolution responses to shared perturbations. ALR can be integrated into different neural PDE solvers by regularizing suitable internal representations, without modifying their backbone architectures. Experiments across multiple PDE benchmarks and neural-operator backbones show that ALR improves prediction accuracy while reducing shared-target discrepancies across rollout origins.
Machine Learning (cs.LG)
arXiv:2610.21370 [cs.LG]
(or arXiv:2610.21370v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.21370 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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