mlsanityData to 14 Oct 2026

Active Learning with Selective Time-Step Acquisition for PDEs

arXiv 2511.18107 ↗First posted 22 Nov 2025cs.LG stat.MLcited by 4

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Abstract (arXiv)

Accurately solving partial differential equations (PDEs) is critical to understanding complex scientific and engineering phenomena, yet traditional numerical solvers are computationally expensive. Surrogate models offer a more efficient alternative, but their development is hindered by the cost of generating sufficient training data from numerical solvers. In this paper, we present a novel framework for active learning in PDE surrogate modeling that reduces this cost. Unlike the existing AL methods for PDEs that always acquire entire PDE trajectories, our approach, STAP (**S**elective **T**ime-Step **A**cquisition for **P**DEs), strategically generates only the most important time steps with the numerical solver, while employing the surrogate model to approximate the remaining steps. This reduces the cost incurred by each trajectory and thus allows the active learning algorithm to try out a more diverse set of trajectories given the same budget. To accommodate this novel framework, we develop an acquisition function that estimates the utility of a set of time steps by approximating its resulting variance reduction. We demonstrate the effectiveness of our method on several benchmark PDEs.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 31 of its 59 references that are in the map. First posted on arXiv 22 Nov 2025.

Builds on

31 of 59 references.

References · 31

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19 more
  1. 2014Bayesian Optimization with Unknown Constraintscited by 109
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  19. 2024Optimal time sampling in physics-informed neural networkscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Trainingcited by 2
  2. 2026Debiased neural operators for estimating functionalscited by 1
  3. 2026Gradient-Informed Temporal Sampling Improves Rollout Accuracy in PDE Surrogate Trainingcited by 0
  4. 2026Data-Efficient Neural Operator Training via Physics-Based Active Learningcited by 0