# Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls

arXiv: https://arxiv.org/abs/2609.31384 · HTML: https://mlsanity.com/paper/2609.31384/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 57 of its 110 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 30 of 57)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Finite Versus Infinite Neural Networks: an Empirical Study](https://mlsanity.com/paper/2007.15801/) (2020)
- [Why M Heads are Better than One: Training a Diverse Ensemble of Deep Networks](https://mlsanity.com/paper/1511.06314/) (2015)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks](https://mlsanity.com/paper/1910.01663/) (2019)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [A Sober Look at LLMs for Material Discovery: Are They Actually Good for Bayesian Optimization Over Molecules?](https://mlsanity.com/paper/2402.05015/) (2024)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Diving into the shallows: a computational perspective on large-scale shallow learning](https://mlsanity.com/paper/1703.10622/) (2017)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [There Will Be a Scientific Theory of Deep Learning](https://mlsanity.com/paper/2604.21691/) (2026)
- [Collaborative Multi-Object Tracking with Conformal Uncertainty Propagation](https://mlsanity.com/paper/2303.14346/) (2023)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [A Unified Comparative Study with Generalized Conformity Scores for Multi-Output Conformal Regression](https://mlsanity.com/paper/2501.10533/) (2025)

## Abstract (arXiv)

Machine learning has become the standard tool for the design of interatomic potentials which balance efficiency and accuracy, but uncertainty quantification remains an open problem. Multiscale simulations introduce an additional challenge: robust uncertainty quantification across scales. Even within one scale, computations are often multistage, producing a sequence of target quantities, each dependent on the previous, and each with some uncertainty. Conformal methods have emerged as a model agnostic framework for recalibrating surrogate predictions to produce sets which contain the truth at a user-specified rate. For multistage workflows, we require uncertainty calibration for multiple chemical properties and atomistic configurations, and we want to propagate uncertainty sets to downstream quantities of interest. Such propagation should capture the error cancellations which occur in many downstream targets in materials science; for instance, an approximate energy difference is often more accurate than individual energy predictions. We present the first exploration of multivariate conformal methods for chemical properties, including Bonferroni-corrected hyperrectangles, hyperellipsoidal sets based on the Mahalanobis distance, and custom loss functions within conformal risk control. Calibration is applied directly to predicted energies, atomic forces, and virial stresses, then propagated to elastic constants and vacancy formation energies employing a variety of commonly considered approximate protocols in materials modeling. We highlight the benefits of building correlation predictions into the conformal procedure, making it possible to build sets which capture near symmetries and error cancellation. We conclude with a discussion of the interplay of the employed approximate computational protocol and conformal guarantees.