VENI, VINDy, VICI: A generative reduced-order modeling framework with uncertainty quantification

Area of Science:

• Computational Science
• Physics-Informed Machine Learning
• Data-Driven Modeling

Background:

• Generative models offer efficient scenario exploration but often lack physical consistency.
• Computational science relies on physical consistency for reliable predictions.
• Existing models struggle to balance data-driven insights with physical laws.

Purpose of the Study:

• To develop a novel physical generative framework for creating physically consistent reduced-order models.
• To integrate data-driven system identification with probabilistic modeling for uncertainty quantification.
• To enhance decision-making in complex physical phenomena by ensuring model reliability.

Main Methods:

• VENI (Variational Encoding of Noisy Inputs): Utilizes variational autoencoders for identifying reduced coordinates from high-dimensional, noisy data.
• VINDy (Variational Identification of Nonlinear Dynamics): Extends sparse system identification with probabilistic modeling for discovering system dynamics.
• VICI (Variational Inference with Credibility Intervals): Enables efficient generation of full-time solutions and provides uncertainty quantification.

Main Results:

• The proposed framework successfully constructs physically consistent reduced-order models.
• Demonstrated effective uncertainty quantification for unseen parameters and initial conditions.
• Validated performance across diverse systems, including chaotic and high-dimensional nonlinear dynamics.

Conclusions:

• The VENI, VINDy, VICI framework offers a robust solution for physically consistent generative modeling.
• This approach enhances the reliability and applicability of generative models in science and engineering.
• It paves the way for more trustworthy and efficient computational exploration of complex physical systems.