{"ID":2884391,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.06981","arxiv_id":"2508.06981","title":"Structure-Preserving Digital Twins via Conditional Neural Whitney Forms","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.","short_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...","url_abs":"https://arxiv.org/abs/2508.06981","url_pdf":"https://arxiv.org/pdf/2508.06981v1","authors":"[\"Brooks Kinch\",\"Benjamin Shaffer\",\"Elizabeth Armstrong\",\"Michael Meehan\",\"John Hewson\",\"Nathaniel Trask\"]","published":"2025-08-09T13:26:44Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.NA\",\"physics.comp-ph\"]","methods":"[\"Diffusion Model\"]","has_code":false}