Parameter Estimation via Adjoint-Based and Machine Learning Methods With Applications to Marine Lakes
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| Argitaratua izan da: | ProQuest Dissertations and Theses (2025) |
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ProQuest Dissertations & Theses
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| Sarrera elektronikoa: | Citation/Abstract Full Text - PDF |
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| Laburpena: | This dissertation presents a comprehensive study on parameter estimation in physical systems, focusing on spatially dependent diffusion coefficients in marine lakes. Two distinct approaches are explored: a classical adjoint-based inverse method and a machine learning-based symbolic regression framework.The first half of the work addresses the recovery of spatially varying eddy diffusivity in the forced heat and screened Poisson equations, which model temperature and salinity dynamics in stratified marine lakes. These lakes are semi-enclosed marine environments characterized by weak tidal exchange and strong vertical stratification, making them ideal systems to study mixing processes. The inverse problem is formulated as a PDE-constrained optimization, and an adjoint-based reduced-space formulation is developed to infer the diffusion coefficient from measured profiles. To mitigate the ill-posedness of the inverse problem, Tikhonov regularization is employed, with the regularization parameter selected via the L-curve method. Synthetic tests demonstrate the accuracy and robustness of the approach, while application to real marine lake data confirms the method’s ability to reconstruct physically meaningful diffusion profiles that align with prior domain knowledge.The second half of the dissertation introduces a reinforcement learning-based symbolic regression framework to discover interpretable governing equations or source terms from data. Traditional symbolic regression methods often rely on a fixed expression library, which can limit their applicability in real-world problems. The proposed approach eliminates this constraint by using an autoregressive model that jointly samples symbolic structures and optimizes associated coefficients. The method is validated on benchmark equation discovery tasks and extended to infer forcing terms in inverse problems. This framework complements the adjoint-based method by enabling interpretable modeling when the governing equations are only partially known or need refinement.Together, these contributions offer robust and interpretable tools for parameter estimation in complex physical systems. The combination of physics-based inversion and data-driven discovery provides a flexible modeling pipeline with applications in geoscience, environmental modeling, and beyond. |
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| ISBN: | 9798297603493 |
| Baliabidea: | ProQuest Dissertations & Theses Global |