Nature Communications · 19 September 2026 · From issue 39
Bayesian bilevel operator learning with low-rank adaptation for efficient uncertainty quantification of PDE inverse problems
In math models, a new method estimates hidden equation values and how confident it is.
Ray Zirui Zhang, Christopher E. Miles et al.
Some science problems work backward: you see an effect, like a tumor's growth pattern, and must guess the hidden rules that caused it. A new computer method guesses these hidden numbers and also reports how confident each guess is. It pairs two steps: one step samples possible answers, and a second step quickly retrains a small neural network to check each guess, using far less computing power than older methods. Tests on math models, including one for tumor growth, showed the method gave accurate answers efficiently.
Shown only on math models and simulations, including a tumor growth model, not real patient data.
Tested only on simulations, including a tumor model, not real patients.
Integrity screen: passed (3 checks) Checked 20 September 2026. Retraction record: none. DOI resolves at doi.org. Metadata record found (Nature Communications). Read the source
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