# Neural Message Passing for Objective-Based Uncertainty Quantification and Optimal Experimental Design

arXiv: https://arxiv.org/abs/2203.07120 · HTML: https://mlsanity.com/paper/2203.07120/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 46 references that are in the map.
- First posted on arXiv 14 Mar 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Scene Graph Generation by Iterative Message Passing](https://mlsanity.com/paper/1701.02426/) (2017)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Holistic 3D Scene Understanding from a Single Image with Implicit Representation](https://mlsanity.com/paper/2103.06422/) (2021)
- [An Efficient Federated Distillation Learning System for Multi-task Time Series Classification](https://mlsanity.com/paper/2201.00011/) (2021)
- [Efficient Bayesian experimentation using an expected information gain lower bound](https://mlsanity.com/paper/1506.00053/) (2015)
- [Quantifying the multi-objective cost of uncertainty](https://mlsanity.com/paper/2010.04653/) (2020)
- [Optimal Experimental Design for Uncertain Systems Based on Coupled Differential Equations](https://mlsanity.com/paper/2007.06117/) (2020)
- [Accelerating Optimal Experimental Design for Robust Synchronization of Uncertain Kuramoto Oscillator Model Using Machine Learning](https://mlsanity.com/paper/2106.00332/) (2021)
- [Phase synchronization of coupled bursting neurons and the generalized Kuramoto model](https://mlsanity.com/paper/1502.04067/) (2015)

## Abstract (arXiv)

Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.