mlsanityData to 14 Oct 2026

Structure-Preserving Digital Twins via Conditional Neural Whitney Forms

arXiv 2508.06981 ↗First posted 9 Aug 2025cs.LG cs.NA math.NAcited by 8

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Abstract (arXiv)

We present a framework for constructing real-time digital twins based on structure-preserving reduced finite element models conditioned on a latent variable Z. The approach uses conditional attention mechanisms to learn both a reduced finite element basis and a nonlinear conservation law within the framework of finite element exterior calculus (FEEC). This guarantees numerical well-posedness and exact preservation of conserved quantities, regardless of data sparsity or optimization error. The conditioning mechanism supports real-time calibration to parametric variables, allowing the construction of digital twins which support closed loop inference and calibration to sensor data. The framework interfaces with conventional finite element machinery in a non-invasive manner, allowing treatment of complex geometries and integration of learned models with conventional finite element techniques. Benchmarks include advection diffusion, shock hydrodynamics, electrostatics, and a complex battery thermal runaway problem. The method achieves accurate predictions on complex geometries with sparse data (25 LES simulations), including capturing the transition to turbulence and achieving real-time inference ~0.1s with a speedup of 3.1x10^8 relative to LES. An open-source implementation is available on GitHub.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 35 of its 88 references that are in the map. First posted on arXiv 9 Aug 2025.

Builds on

35 of 88 references.

References · 35

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23 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 6.

8 papers.

  1. 2026Structure-Preserving Learning Improves Geometry Generalization in Neural PDEscited by 8
  2. 2025Physics-informed sensor coverage through structure preserving machine learningcited by 3
  3. 2025Multi-robot Multi-source Localization in Complex Flows with Physics-Preserving Environment Modelscited by 1
  4. 2026A meshfree exterior calculus for generalizable and data-efficient learning of physics from point cloudscited by 1
  5. 2026A Hybridizable Neural Time Integrator for Stable Autoregressive Forecastingcited by 0
  6. 2026Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEscited by 0
  7. 2026Neural Navigation Functions for Zero-Shot Generalizable Motion Planningcited by 0
  8. 2026Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantificationcited by 0