Benchmarking Long Roll-outs of Auto-regressive Neural Operators for the Compressible Navier-Stokes Equations with Conserved Quantity Correction
Deep learning has been proposed as an efficient alternative for the numerical approximation of PDE solutions, offering fast, iterative simulation of PDEs through the approximation of solution operators. However, deep learning solutions have struggle to perform well over long prediction durations due to the accumulation of auto-regressive error, which is compounded by the inability of models to conserve physical quantities. In this work, we present conserved quantity correction, a model-agnostic technique for incorporation physical conservation criteria within deep learning models. Our results demonstrate consistent improvement in the long-term stability of auto-regressive neural operator models, regardless of the model architecture. Furthermore, we analyze the performance of neural operators from the spectral domain, highlighting significant limitations of present architectures. These results highlight the need for future work to consider architectures that place specific emphasis on high frequency components, which are integral to the understanding and modeling of turbulent flows.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Generative Scenario Rollouts for End-to-End Autonomous Driving
Vision-Language-Action (VLA) models are emerging as highly effective planning models for end-to-end autonomous driving systems. However, current works mostly rely on imitation learning from sparse trajectory annotations …
Reinforcement LearningAutonomous DrivingExploring Design Choices for Autoregressive Deep Learning Climate Models
Deep Learning models have achieved state-of-the-art performance in medium-range weather prediction but often fail to maintain physically consistent rollouts beyond 14 days. In contrast, a few atmospheric models demonstra…
Deep LearningMemory-Conditioned Flow-Matching for Stable Autoregressive PDE Rollouts
Autoregressive generative PDE solvers can be accurate one step ahead yet drift over long rollouts, especially in coarse-to-fine regimes where each step must regenerate unresolved fine scales. This is the regime of diffus…
Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos
Autoregressive surrogate models (or \textit{emulators}) of spatiotemporal systems provide an avenue for fast, approximate predictions, with broad applications across science and engineering. At inference time, however, t…
DenoisingAutoregression-Free Neural Operators for Time-Dependent PDEs
Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform…