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Updated: Jan 20, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

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Published on: September 7, 2019

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

Paolo Conti¹, Jonas Kneifl², Andrea Manzoni¹

¹MOX - Department of Mathematics, Politecnico di Milano, Milan, Italy.

Neural Networks : the Official Journal of the International Neural Network Society

|January 18, 2026

Summary

This summary is machine-generated.

We introduce a new framework for generative models that ensures physical consistency in scientific predictions. This approach integrates data-driven methods with probabilistic modeling for accurate, uncertainty-aware reduced-order models.

Keywords:

Data-driven methods Generative AI Nonlinear dynamics Reduced-order modeling Sparse system identification Variational autoencoders

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Last Updated: Jan 20, 2026

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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.