# Filtered Neural Galerkin model reduction schemes for efficient propagation of initial condition uncertainties in digital twins

arXiv: https://arxiv.org/abs/2511.00670 · HTML: https://mlsanity.com/paper/2511.00670/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 14 of 14)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale](https://mlsanity.com/paper/2012.05841/) (2020)
- [Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equations](https://mlsanity.com/paper/2203.01360/) (2022)
- [Evolutional Deep Neural Network](https://mlsanity.com/paper/2103.09959/) (2021)
- [Bayesian operator inference for data-driven reduced-order modeling](https://mlsanity.com/paper/2204.10829/) (2022)
- [Inverse Problems and Data Assimilation](https://mlsanity.com/paper/1810.06191/) (2018)
- [Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks](https://mlsanity.com/paper/2310.04867/) (2023)
- [CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations](https://mlsanity.com/paper/2402.14646/) (2024)
- [Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes](https://mlsanity.com/paper/2306.15630/) (2023)
- [A digital twin framework for civil engineering structures](https://mlsanity.com/paper/2308.01445/) (2023)
- [Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations](https://mlsanity.com/paper/2404.01145/) (2024)
- [Predictive Digital Twins with Quantified Uncertainty for Patient-Specific Decision Making in Oncology](https://mlsanity.com/paper/2505.08927/) (2025)

## Built on by (most cited first, 1 of 1)

- [MAD-NG: Meta-Auto-Decoder Neural Galerkin Method for Solving Parametric Partial Differential Equations](https://mlsanity.com/paper/2512.21633/) (2025)

## Abstract (arXiv)

Uncertainty quantification in digital twins is critical to enable reliable and credible predictions beyond available data. A key challenge is that ensemble-based approaches can become prohibitively expensive when embedded in control and data assimilation loops in digital twins, even when reduced models are used. We introduce a reduced modeling approach that advances in time the mean and covariance of the reduced solution distribution induced by the initial condition uncertainties, which eliminates the need to maintain and propagate a costly ensemble of reduced solutions. The mean and covariance dynamics are obtained as a moment closure from Neural Galerkin schemes on pre-trained neural networks, which can be interpreted as filtered Neural Galerkin dynamics analogous to Gaussian filtering and the extended Kalman filter. Numerical experiments demonstrate that filtered Neural Galerkin schemes achieve more than one order of magnitude speedup compared to ensemble-based uncertainty propagation.