Nudging with learned surrogate dynamics converges exponentially to an explicit error floor determined by surrogate error and observation noise, with training data requirements quantified for noise-free cases.
Continuous Data Assimilation for Semilinear Parabolic Equations with Multiplicative Observation Noise
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abstract
The problem of continuous data assimilation for semilinear parabolic equations based on partial observations corrupted by noise is investigated. The noise is allowed to be multiplicative, with additive noise arising as a special case. In a general Gelfand triple framework, an abstract theory for the nudging equation is developed that covers both weak and strong formulations. Mean square convergence of the assimilation error is proved under suitable assumptions, and, under additional integrability conditions on the noise, a uniform almost sure convergence result is established. Finally, the framework is applied to several PDE models, including the 2D Navier-Stokes, 2D magnetohydrodynamics, 2D quasi-geostrophic, and 1D Allen-Cahn equations.
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math.DS 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Continuous Data Assimilation with Learned Surrogate Dynamics
Nudging with learned surrogate dynamics converges exponentially to an explicit error floor determined by surrogate error and observation noise, with training data requirements quantified for noise-free cases.