Recovering Governing Equations from Solution Data: Identifiability Bounds for Linear and Nonlinear ODEs
arXiv:2606.27285v1 Announce Type: new Abstract: Learning governing equations from observed solution data is a fundamental challenge in scientific machine learning \cite{bruntonDiscoveringGoverningEquations2016,kovachkiNeuralOperatorLearning2023,longPDENetLearningPDEs2018,rudyDatadrivenDiscoveryPartial2017,raonicConvolutionalNeuralOperators2023}, yet the theoretical conditions under which a ground-truth ODE can be uniquely and stably identified from multiple solution observations remain largely undeveloped, and no quantitative analysis of the sample complexity of such learning tasks exists in t
The proliferation of scientific machine learning and data-driven discovery necessitates a deeper theoretical understanding of model identifiability to ensure robust and reliable AI systems.
This research addresses a fundamental theoretical challenge in scientific machine learning, providing conditions for unique and stable identification of governing equations, which is critical for trustworthy AI in scientific contexts.
The ability to uniquely and stably identify underlying differential equations from solution data will improve the reliability and interpretability of scientific machine learning models, moving beyond purely correlational approaches.
- · Scientific machine learning researchers
- · Pharma and biotech (drug discovery)
- · Materials science
- · AI model developers
- · Developers of unstable or unidentifiable data-driven models
- · Fields relying solely on black-box correlational AI
Improved accuracy and trustworthiness of AI systems used for scientific discovery and engineering design.
Accelerated development of novel materials, personalized medicines, and more efficient industrial processes based on verified physical principles.
Enhanced automation of scientific experimentation and hypothesis generation, reducing the time and cost for breakthroughs across various scientific disciplines.
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