DIVIDE: A Framework for Learning from Independent Multi-Mechanism Data Using Deep Encoders and Gaussian Processes

2025-11-16

AI Summary

Scientific data are often governed by multiple independent generative mechanisms—e.g., spatial, categorical, and structural—whose coupled effects hinder disentanglement of individual contributions. To address this, we propose a mechanism-aware deep Gaussian process (DGPs) model: input data are mapped via mechanism-specific deep encoders into a shared latent space, where a structured Gaussian process prior explicitly encodes both independent mechanistic effects and their nonlinear interactions (e.g., additive or multiplicative). The model enables interpretable mechanistic decomposition, uncertainty-calibrated prediction, and efficient active learning. We validate it on synthetic benchmarks, ferroelectric spin simulations, and experimental piezoresponse force microscopy hysteresis loops. Results demonstrate robust disentanglement of multi-mechanism influences, accurate recovery of ground-truth interaction forms, and strong performance under noise—outperforming standard DGPs and mechanistic baselines.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Mechanism Design

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Scientific datasets often arise from multiple independent mechanisms such as spatial, categorical or structural effects, whose combined influence obscures their individual contributions. We introduce DIVIDE, a framework that disentangles these influences by integrating mechanism-specific deep encoders with a structured Gaussian Process in a joint latent space. Disentanglement here refers to separating independently acting generative factors. The encoders isolate distinct mechanisms while the Gaussian Process captures their combined effect with calibrated uncertainty. The architecture supports structured priors, enabling interpretable and mechanism-aware prediction as well as efficient active learning. DIVIDE is demonstrated on synthetic datasets combining categorical image patches with nonlinear spatial fields, on FerroSIM spin lattice simulations of ferroelectric patterns, and on experimental PFM hysteresis loops from PbTiO3 films. Across benchmarks, DIVIDE separates mechanisms, reproduces additive and scaled interactions, and remains robust under noise. The framework extends naturally to multifunctional datasets where mechanical, electromagnetic or optical responses coexist.

Problem

• Disentangles independent multi-mechanism influences in scientific datasets
• Separates combined effects using deep encoders and Gaussian Processes
• Handles categorical, spatial, and structural mechanisms with uncertainty quantification

Innovation

• Deep encoders separate independent mechanisms
• Gaussian Process captures combined effects with uncertainty
• Joint latent space enables interpretable mechanism-aware prediction