ArticlePhilosophical transactions. Series A, Mathematical, physical, and engineering sciences2025
Assessment of uncertainty quantification in universal differential equations.
Article in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
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Who cites it
6 citing papers in PubMed.
- Universal differential equations for quantifying NF-κB-p53 signaling crosstalk.Bioinformatics (Oxford, England) · 2026Article
- A novel approach to quantify out-of-distribution uncertainty in Neural and Universal Differential Equations.NPJ systems biology and applications · 2026Article
- Current state and open problems in universal differential equations for systems biology.NPJ systems biology and applications · 2025Article
- Conditional universal differential equations capture population dynamics and interindividual variation in c-peptide production.NPJ systems biology and applications · 2025Article
- Assessment of uncertainty quantification in universal differential equations.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Article
- Preface to the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
4 authors.
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Abstract
Scientific machine learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques to uncover the governing equations of complex processes. Among the available approaches, universal differential equations (UDEs) combine prior knowledge in the form of mechanistic formulations with universal function approximators, such as neural networks. Integral to the efficacy of UDEs is the joint estimation of parameters for both the mechanistic formulations and the universal function approximators using empirical data. However, the robustness and applicability of these resultant models hinge upon the rigorous quantification of uncertainties associated with their parameters and predictive capabilities. In this work, we provide a formalization of uncertainty quantification (UQ) for UDEs and investigate key frequentist and Bayesian methods. By analyzing three synthetic examples of varying complexity, we evaluate the validity and efficiency of ensembles, variational inference and Markov-chain Monte Carlo sampling as epistemic UQ methods for UDEs.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.