Graphical conditional generative modeling for digital twin modeling

2026-06-15

AI Summary

This work addresses the challenges of complexity and poor interpretability in digital twin modeling, which often arise from high-dimensional inputs, heterogeneous data, and multi-timescale dynamics—particularly in control and data assimilation tasks under uncertainty. The authors propose an iterative sparsification method grounded in conditional generative modeling and Gaussian process variance decomposition (kernel ANOVA). This approach identifies input variables that critically shape the full conditional distribution of target outputs—including their variability, tail behavior, and multimodality—and automatically discovers a compact state-action-memory structure that enables approximate Markovian dynamics in control settings. The resulting parsimonious stochastic surrogate models exhibit both strong interpretability and high predictive performance, matching or closely approaching the downstream accuracy of full-variable models across diverse benchmarks, including stochastic dynamical systems, PDE-based control, reinforcement learning, and economic datasets.

Abstract

Digital twin modeling, including control and data assimilation under model uncertainty, often faces an open-ended fidelity problem: adding variables, data streams, and time scales can indefinitely increase model complexity, ultimately producing systems that are difficult to maintain, validate, interpret, and use for stress or safety testing. As an alternative, one can seek parsimonious stochastic surrogate models built only on the variables needed to describe the relevant quantities of interest. We introduce a framework for discovering such variables from observational data by identifying which candidate inputs influence the full conditional law of a target quantity, rather than only its conditional mean. This distinction is essential in stochastic, coarse-grained, or partially observed systems, where dependencies may appear through changes in variability, tail behavior, multimodality, or uncertainty rather than through deterministic functional relationships. The framework couples conditional generative modeling, which learns the conditional distribution of the target given candidate inputs, with Gaussian-process-based analysis of variance (through kernel mode decomposition), which enables iterative pruning of non-influential inputs and interpretable structure discovery. In control settings, the resulting surrogate can be interpreted as a learned Markov decision process: the method identifies not only a transition model, but also the state, action, and memory variables needed to make the learned dynamics effectively Markovian. Across examples involving stochastic dynamical systems, missing variables, PDE control, reinforcement learning, and economic data, the discovered structures yield interpretable stochastic surrogates whose downstream performance is comparable to models trained on the full variable set.

Problem

• digital twin
• model complexity
• fidelity problem
• stochastic systems
• conditional generative modeling

Innovation

• conditional generative modeling
• digital twin
• Gaussian process ANOVA
• Markov decision process
• stochastic surrogate