analiza aiqbench
This research introduces Online Generative Active Sampling (OGAS), a method that uses a parallel diffusion model to dynamically steer data generation toward high-difficulty PDE regimes during online training. By actively sampling challenging trajectories rather than relying on uniform distribution, the approach significantly improves tail statistics and worst-case reliability without incurring wall-time overhead. The technique is particularly relevant for applications requiring robust generalization across complex physical configurations, such as fluid dynamics and reaction-diffusion systems.
Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training
arXiv:2606.09949v1 Announce Type: new Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers. However, when the surrogate's goal is to generalize across a wide range of PDE configurations (e.g., initial conditions and physical coefficients), generating a representative training set is non-trivial. Uniform sampling of configuration parameters often under-represents trajectories exhibiting challenging dynamics, leading to high prediction errors and large error variance in the trained surrogate. Online training, where data generation and surrogate training are coupled, offers a natural advantage by allowing solver parameters to be steered on-the-fly. To efficiently exploit this capability, we introduce Online Generative Active Sampling (OGAS), an active learning method that reactively learns the relationship between configuration parameters and surrogate performance to control the sampling distribution. OGAS trains a fast diffusion model in parallel to the surrogate to act as a conditional sampler, mapping a surrogate-derived difficulty signal (e.g., loss or uncertainty) to configuration parameters. By actively drawing target signals from a prior biased toward high difficulty, OGAS continuously steers data generation toward challenging regimes without delaying the training workflow. We evaluate OGAS across 2D PDEs with distinct challenging dynamics (Kuramoto-Sivashinsky, Navier-Stokes, Gray-Scott) and up to 308 parameters, using multiple surrogate architectures. Across all settings, OGAS consistently improves tail statistics, yielding substantial reductions in errors above the 99th percentile and overall error dispersion compared to uniform sampling. While prioritizing challenging trajectories introduces a trade-off with average error, OGAS effectively ensures worst-case reliability of trained surrogates with negligible wall-time overhead.
Abstract:Data-driven PDE surrogates are trained with data produced by numerical PDE solvers. However, when the surrogate's goal is to generalize across a wide range of PDE configurations (e.g., initial conditions and physical coefficients), generating a representative training set is non-trivial. Uniform sampling of configuration parameters often under-represents trajectories exhibiting challenging dynamics, leading to high prediction errors and large error variance in the trained surrogate. Online training, where data generation and surrogate training are coupled, offers a natural advantage by allowing solver parameters to be steered on-the-fly. To efficiently exploit this capability, we introduce Online Generative Active Sampling (OGAS), an active learning method that reactively learns the relationship between configuration parameters and surrogate performance to control the sampling distribution. OGAS trains a fast diffusion model in parallel to the surrogate to act as a conditional sampler, mapping a surrogate-derived difficulty signal (e.g., loss or uncertainty) to configuration parameters. By actively drawing target signals from a prior biased toward high difficulty, OGAS continuously steers data generation toward challenging regimes without delaying the training workflow. We evaluate OGAS across 2D PDEs with distinct challenging dynamics (Kuramoto-Sivashinsky, Navier-Stokes, Gray-Scott) and up to 308 parameters, using multiple surrogate architectures. Across all settings, OGAS consistently improves tail statistics, yielding substantial reductions in errors above the 99th percentile and overall error dispersion compared to uniform sampling. While prioritizing challenging trajectories introduces a trade-off with average error, OGAS effectively ensures worst-case reliability of trained surrogates with negligible wall-time overhead.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.09949 [cs.LG]
(or arXiv:2606.09949v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.09949 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 336 cuvinte
Subiecte conexe
Quantifying the Impact of Lossy Compression on Neural Generative Surrogate Modeling
arXiv · 16 iun. 2026
One-Step Generative Surrogate Models via Block-Triangular Joint Drifting
arXiv · 23 sept. 2026
Autoregressive One-Step Generative Modeling for Dynamical System Forecasting
arXiv · 28 iul. 2026
Large Discovery Models: Empirically-grounded Model-Based Open-Ended Search
arXiv · 19 aug. 2026