mlsanityData to 13 Oct 2026

Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discovery

arXiv 2308.10283 ↗First posted 20 Aug 2023cs.LG physics.comp-phcited by 6

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Abstract (arXiv)

We propose a new parameter-adaptive uncertainty-penalized Bayesian information criterion (UBIC) to prioritize the parsimonious partial differential equation (PDE) that sufficiently governs noisy spatial-temporal observed data with few reliable terms. Since the naive use of the BIC for model selection has been known to yield an undesirable overfitted PDE, the UBIC penalizes the found PDE not only by its complexity but also the quantified uncertainty, derived from the model supports' coefficient of variation in a probabilistic view. We also introduce physics-informed neural network learning as a simulation-based approach to further validate the selected PDE flexibly against the other discovered PDE. Numerical results affirm the successful application of the UBIC in identifying the true governing PDE. Additionally, we reveal an interesting effect of denoising the observed data on improving the trade-off between the BIC score and model complexity. Code is available at https://github.com/Pongpisit-Thanasutives/UBIC.

Key facts. Cited by 6 papers in the map (data through 13 Oct 2026). Builds on 25 of its 68 references that are in the map. First posted on arXiv 20 Aug 2023.

Builds on

25 of 68 references.

References · 25

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13 more
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Cited by year (2026 to 13 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 5.

6 papers.

  1. 2026Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offscited by 2
  2. 2024On uncertainty-penalized Bayesian information criterioncited by 1
  3. 2026Dynamics-aware identification of governing equations from sparse and noisy datacited by 1
  4. 2026Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operatorscited by 0
  5. 2026Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selectioncited by 0
  6. 2026Exact Algebraic Computation of Learning Coefficients for Two-Dimensional Singular Modelscited by 0