VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantification
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Generative models are increasingly transforming science and engineering by enabling low-cost synthesis and exploration of new scenarios for complex physical phenomena. While they can deliver uncertainty-aware predictions to aid decision making, they often fail to preserve physical consistency, which is a core requirement in computational science. We introduce VENI, VINDy, VICI, a physical generative framework that couples data-driven system identification with a probabilistic modelling pipeline to build physically consistent and efficient reduced-order models with uncertainty quantification. We first use VENI (Variational Encoding of Noisy Inputs), based on variational autoencoders, to extract reduced coordinates from high-dimensional, noisy measurements. In parallel, VINDy (Variational Identification of Nonlinear Dynamics) extends sparse system identification by embedding probabilistic inference into the discovery of governing dynamics. Finally, VICI (Variational Inference with Credibility Intervals) enables efficient generation of full time solutions and provides uncertainty quantification for unseen parameters and initial conditions. We demonstrate the effectiveness of the proposed framework on chaotic and high-dimensional nonlinear systems, including applications in fluid dynamics and micro electro-mechanical systems (MEMS). Reduced-order modeling \sep data-driven methods \sep variational autoencoders \sep sparse system identification \sep nonlinear dynamics \sep generative AI.
