Structure-Preserving Digital Twins via Conditional Neural Whitney Forms
This work addresses the need for efficient and reliable digital twins in engineering applications like battery thermal runaway, though it is incremental as it builds on existing finite element and machine learning techniques.
The paper tackles the problem of constructing real-time digital twins by developing a framework that uses conditional attention mechanisms to learn reduced finite element models, ensuring exact preservation of conserved quantities and numerical well-posedness. It achieves accurate predictions on complex geometries with sparse data, such as a speedup of 3.1x10^8 relative to LES and real-time inference in ~0.1s.
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.