Data-driven stochastic reduced-order modeling of parametrized dynamical systems

2026-01-15

AI Summary

This work addresses the computational expense of high-fidelity simulations in parametric stochastic dynamical systems and the inability of existing reduced-order models to adequately handle stochasticity or quantify uncertainty. The authors propose a data-driven framework that jointly learns a probabilistic autoencoder and a stochastic differential equation in the latent space via amortized stochastic variational inference, yielding a continuous-time stochastic reduced-order model capable of generalizing to unseen parameters and forcing conditions. By introducing a Markovian Gaussian process reparameterization, the method eliminates the need for costly forward solvers, enables incorporation of physical priors, and achieves computational complexity independent of both data size and system stiffness. Evaluated on three challenging benchmarks, the approach significantly outperforms state-of-the-art methods, demonstrating breakthroughs in both generalization capability and computational efficiency.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle with stochastic dynamics and fail to quantify prediction uncertainty, limiting their utility in robust decision-making contexts. To address these challenges, we introduce a data-driven framework for learning continuous-time stochastic ROMs that generalize across parameter spaces and forcing conditions. Our approach, based on amortized stochastic variational inference, leverages a reparametrization trick for Markov Gaussian processes to eliminate the need for computationally expensive forward solvers during training. This enables us to jointly learn a probabilistic autoencoder and stochastic differential equations governing the latent dynamics, at a computational cost that is independent of the dataset size and system stiffness. Additionally, our approach offers the flexibility of incorporating physics-informed priors if available. Numerical studies are presented for three challenging test problems, where we demonstrate excellent generalization to unseen parameter combinations and forcings, and significant efficiency gains compared to existing approaches.

Problem

• stochastic dynamics
• reduced-order modeling
• uncertainty quantification
• parametrized dynamical systems
• data-driven modeling

Innovation

• stochastic reduced-order modeling
• amortized variational inference
• Markov Gaussian processes
• physics-informed priors
• latent stochastic dynamics