ArticleNature computational science2024
A scalable framework for learning the geometry-dependent solution operators of partial differential equations.
Article in Nature computational science, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers, 1 of them a synthesis that pooled it.
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Who cites it
17 citing papers in PubMed, 1 synthesis or guideline pooled it.
- Technologies, Clinical Applications, and Implementation Barriers of Digital Twins in Precision Cardiology: Systematic Review.JMIR cardio · 2026Pooled it
- An eikonal model with re-excitability for fast simulations in cardiac electrophysiology.The Journal of physiology · 2026Article
- The Hodgkin-Huxley-Katz Prize Lecture: Heart digital twins: A new paradigm in arrhythmia medicine.The Journal of physiology · 2026Article
- Toward nonlinear representations with Gaussian-splat manifolds for physics-informed learning.Nature communications · 2026Article
- A physics-informed eikonal model for simulating arrhythmias in the human heart in real-time.Nature communications · 2026Article
- 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
- Digital heart initiative: an ecosystem for digital discovery and precision medicine in cardiology.National science review · 2026Article
- Towards mechanisms-driven strategy for persistent atrial fibrillation ablation: Leveraging digital twins.Journal of precision medicine (Amsterdam, Netherlands) · 2026Article
- FunDiff: diffusion models over function spaces for physics-informed generative modeling.Nature communications · 2026Article
- Rapid prediction of cardiac activation in the left ventricle with geometric deep learning: a step towards cardiac resynchronization therapy planning.NPJ digital medicine · 2026Article
- Bio-inspired unified model for representing geometric relations in robotic perception.Scientific reports · 2026Article
- China runoff-field forecasting based on cross-scale gating and basin-topology attention.PloS one · 2026Article
- Developing cardiac biomechanical models beyond the clinic: modeling stressors of daily life.Biomechanics and modeling in mechanobiology · 2025Review
- Computational modelling of biological systems now and then: revisiting tools and visions from the beginning of the century.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Review
- HETEROGENEOUS PERIDYNAMIC NEURAL OPERATORS: DISCOVER BIOTISSUE CONSTITUTIVE LAW AND MICROSTRUCTURE FROM DIGITAL IMAGE CORRELATION MEASUREMENTS.Foundations of data science (Springfield, Mo.) · 2025Article
- Fast and accurate prediction of drug induced proarrhythmic risk with sex specific cardiac emulators.NPJ digital medicine · 2024Article
- A scalable framework for learning the geometry-dependent solution operators of partial differential equations.Nature computational science · 2024Article
Corrections and comments
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Authors and funding
6 authors.
Funding
Abstract
Solving partial differential equations (PDEs) using numerical methods is a ubiquitous task in engineering and medicine. However, the computational costs can be prohibitively high when many-query evaluations of PDE solutions on multiple geometries are needed. Here we aim to address this challenge by introducing Diffeomorphic Mapping Operator Learning (DIMON), a generic artificial intelligence framework that learns geometry-dependent solution operators of different types of PDE on a variety of geometries. We present several examples to demonstrate the performance, efficiency and scalability of the framework in learning both static and time-dependent PDEs on parameterized and non-parameterized domains; these include solving the Laplace equations, reaction-diffusion equations and a system of multiscale PDEs that characterize the electrical propagation on thousands of personalized heart digital twins. DIMON can reduce the computational costs of solution approximations on multiple geometries from hours to seconds with substantially less computational resources.
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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.