Structure-Preserving Digital Twins via Conditional Neural Whitney Forms

• URL: http://arxiv.org/abs/2508.06981v1
• Date: Sat, 09 Aug 2025 13:26:44 GMT
• Title: Structure-Preserving Digital Twins via Conditional Neural Whitney Forms
• Authors: Brooks Kinch, Benjamin Shaffer, Elizabeth Armstrong, Michael Meehan, John Hewson, Nathaniel Trask,
• Abstract summary: We present a framework for constructing real-time digital twins based on structure-preserving reduced finite element models conditioned on a latent variable Z.<n>The approach uses conditional attention mechanisms to learn both a reduced finite element basis and a nonlinear conservation law.<n>The framework interfaces with conventional finite element machinery in a non-invasive manner, allowing treatment of complex geometries.
• Score: 0.8796261172196743
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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