Hybridndiff-UQ: Uncertainty quantification for hybrid neural differentiable modeling.

Area of Science:

• Scientific Machine Learning
• Computational Physics
• Data-Driven Modeling

Background:

• Hybrid neural differentiable models integrate physics into deep neural networks for advanced predictive capabilities.
• Quantifying uncertainties in these models is a critical, unaddressed challenge for reliable data-driven modeling.
• Existing methods struggle to effectively propagate and estimate uncertainties from various sources.

Purpose of the Study:

• To introduce a novel method for uncertainty quantification in hybrid neural differentiable modeling.
• To effectively and efficiently propagate and estimate both aleatoric and epistemic uncertainties.
• To provide a scalable and implementable framework for Bayesian learning in complex physical systems.

Main Methods:

• Leveraging deep ensemble Bayesian learning and nonlinear transformations for uncertainty estimation.
• Modeling aleatoric uncertainties using hybrid neural models and unscented transformations for propagation.
• Estimating epistemic uncertainties via an ensemble of stochastic gradient descent trajectories for posterior approximation.

Main Results:

• The proposed method successfully discerns and quantifies both aleatoric and epistemic uncertainties.
• It provides a practical approximation to the posterior distribution of network and physical parameters.
• Demonstrated effectiveness on problems governed by ordinary and partial differential equations.

Conclusions:

• The novel uncertainty quantification method enhances the reliability of hybrid neural differentiable models.
• The framework is simple to implement, scalable, and suitable for parallel computing.
• This advancement is crucial for robust data-driven modeling in complex scientific domains.