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Machine Learning for Inverse Problems and Data Assimilation
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The aim of this book is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems and/or data assimilation who wish to see a mathematical presentation of machine learning as it pertains to their fields. As a by-product, we include a succinct mathematical treatment of various fundamental underpinning topics in machine learning, and adjacent areas of (computational) mathematics.
Forward citations
Cited by 2 Pith papers
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Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems
Under a squeezing condition on the dynamics, a discrete-time square-root ensemble Kalman filter (and its surrogate-model variant) achieves long-time mean state estimation error of order ε, the observation noise level,...
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Flow Matching for Efficient and Scalable Data Assimilation
A training-free flow matching data assimilation filter, EnFF, generalizes the bootstrap particle filter and ensemble Kalman filter and reports improved cost-accuracy tradeoffs on high-dimensional benchmarks.
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