Structure-Preserving Digital Twins via Conditional Neural Whitney Forms

2025-08-09

AI Summary

Digital twins struggle to simultaneously ensure numerical well-posedness, exact conservation-law preservation, and real-time parameter calibration under sparse data and optimization errors. Method: This paper proposes a structure-preserving real-time modeling framework based on the conditional neural Whitney form, integrating finite element exterior calculus (FEEC) with latent-variable conditioning. A conditional attention network jointly learns reduced-order bases and nonlinear conservation laws, rigorously enforcing geometric structure preservation, physical quantity conservation, and numerical stability. The framework is compatible with conventional finite element toolchains and supports closed-loop inference and online sensor calibration. Results: On merely 25 large-eddy simulation (LES) snapshots, the framework achieves prediction errors below 1.2% across diverse problems—including advection-diffusion, shock dynamics, and battery thermal runaway—while requiring only ~0.1 seconds per inference step, yielding a speedup of up to 3.1×10⁸× over full-scale LES.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Construct real-time digital twins using structure-preserving models
• Learn reduced finite element basis with conditional attention mechanisms
• Achieve accurate predictions on complex geometries with sparse data

Innovation

• Conditional attention mechanisms for FEEC
• Real-time calibration to parametric variables
• Non-invasive integration with finite elements