Structure-Preserving Digital Twins via Conditional Neural Whitney Forms
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915437434896384 |
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| author | Kinch, Brooks Shaffer, Benjamin Armstrong, Elizabeth Meehan, Michael Hewson, John Trask, Nathaniel |
| author_facet | Kinch, Brooks Shaffer, Benjamin Armstrong, Elizabeth Meehan, Michael Hewson, John Trask, Nathaniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure-Preserving Digital Twins via Conditional Neural Whitney Forms Kinch, Brooks Shaffer, Benjamin Armstrong, Elizabeth Meehan, Michael Hewson, John Trask, Nathaniel Machine Learning Numerical Analysis Computational Physics 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. |
| title | Structure-Preserving Digital Twins via Conditional Neural Whitney Forms |
| topic | Machine Learning Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2508.06981 |