ArticleNature communications2025
One-shot learning for solution operators of partial differential equations.
Article in Nature communications, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
What it found
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Who cites it
4 citing papers in PubMed.
- Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization.IEEE transactions on evolutionary computation : a publication of the IEEE Neural Networks Council · 2026Article
- FunDiff: diffusion models over function spaces for physics-informed generative modeling.Nature communications · 2026Article
- China runoff-field forecasting based on cross-scale gating and basin-topology attention.PloS one · 2026Article
- MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics.Computer methods in applied mechanics and engineering · 2023Article
Corrections and comments
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Authors and funding
5 authors.
Funding
Abstract
Learning and solving governing equations of a physical system, represented by partial differential equations (PDEs), from data is a central challenge in many areas of science and engineering. Traditional numerical methods can be computationally expensive for complex systems and require complete governing equations. Existing data-driven machine learning methods require large datasets to learn a surrogate solution operator, which could be impractical. Here, we propose a solution operator learning method that requires only one PDE solution, i.e., one-shot learning, along with suitable initial and boundary conditions. Leveraging the locality of derivatives, we define a local solution operator in small local domains, train it using a neural network, and use it to predict solutions of new input functions via mesh-based fixed-point iteration or meshfree neural-network based approaches. We test our method on various PDEs, complex geometries, and a practical spatial infection spread application, demonstrating its effectiveness and generalization capabilities.
Identifiers
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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.