Jonas Kneifl and Paolo Conti present a new method for creating efficient and interpretable models of complex systems in their study, titled “VENI, VINDy, VICI – a variational reduced-order modeling framework with uncertainty quantification.” These models help understand and predict the behavior of these complex systems more rapidly and reliably.
This work is the result of an international and interdisciplinary collaboration between SimTech at the University of Stuttgart, the Politecnico di Milano, Italy, and the University of Washington, US. Paolo Conti, a doctoral researcher at the Department of Civil and Environmental Engineering at Politecnico di Milano, and Jonas Kneifl, a doctoral researcher at SimTech from the Institute of Engineering and Computational Mechanics (ITM), started this project at the AI Institute in Dynamic Systems during a research stay at the University of Washington.
They have developed a data-driven, non-intrusive framework for building reduced-order models (ROMs). These models help simplify complex systems by identifying key variables and their interactions in an interpretable manner while also quantifying the uncertainty in the predictions. Their innovative approach leverages variational autoencoders for reducing the dimensionality of data and introduces a probabilistic method called Variational Identification of Nonlinear Dynamics (VINDy) to pinpoint the dynamics at play.
The framework, named VENI, VINDy, VICI, consists of three main components:
- VENI (Variational Encoding of Noisy Inputs): This component uses variational autoencoders to convert high-dimensional, noisy data into a lower-dimensional space, enabling an efficient approximation of the dynamics.
- VINDy (Variational Identification of Nonlinear Dynamics): This part introduces a probabilistic method to identify the underlying dynamics governing the reduced data, using techniques that ensure the model is both understandable and robust to uncertainties.
- VICI (Variational Inference with Certainty Intervals): This component provides uncertainty-aware estimates, thanks to a probabilistic representation of the system states and dynamics.
The study showcases the effectiveness of the VENI, VINDy, VICI framework through applications to both the Rössler system, a well-known chaotic system, and high-dimensional partial differential equation (PDE) benchmarks in structural mechanics and fluid dynamics. These applications highlight the framework's ability to create accurate and understandable models from complex, noisy data.
This preprint is significant not only for its technical contributions but also for its broader relevance. By improving the reliability and interpretability of simulations that model complex phenomena, their framework can enhance our understanding and management of various engineering and scientific challenges.
Read the full preprint to explore the detailed methodology and results of their research: https://doi.org/10.48550/ARXIV.2405.20905.
Authors: Paolo Conti*, Jonas Kneifl*, Andrea Manzoni, Attilio Frangi, Jörg Fehr, Steven L. Brunton, J. Nathan Kutz
*These authors contributed equally to this work and are listed in alphabetical order.