| Abstract: |
| The rapidly increasing volume and complexity of biomedical data, characterized by its multiscale and multidimensional nature, present significant opportunities and challenges for effective model development. Multiscale systems in biomedicine often exhibit complex dynamics that cannot be adequately captured by traditional modeling approaches, thereby necessitating novel data-driven model reduction techniques. Furthermore, the sparse, heterogeneous, and often incomplete nature of biomedical datasets adds layers of complexity, underscoring the need for advanced methodologies capable of extracting meaningful patterns and representing system dynamics across multiple scales.
In this work, we present a systematic methodology for identifying regions within the data where reduced models can be effectively constructed, leveraging tools from the Computational Singular Perturbation (CSP) method. By segmenting the data and pinpointing distinct regions of dynamic behavior, our approach facilitates the construction of region-specific reduced models that accurately represent the local properties of the system. This strategy is particularly effective in addressing the inherent multiscale complexity of biological systems, allowing for the development of reduced models that are computationally efficient while retaining the critical features of the underlying dynamics.
The proposed methodology employs data-driven techniques to approximate key components, such as the Jacobian matrix, which plays a vital role in identifying timescale separations and dominant subprocesses in the data. By integrating CSP tools, we ensure a systematic partitioning of the data into regions where different reduced models can be reliably constructed, thereby enhancing both the validity and applicability of these models. After identifying the correct data partitioning, we can apply existing numerical methods to reconstruct the corresponding governing equations of the reduced models. This structured approach bridges the gap between data sparsity, multiscale interactions, and model complexity, ultimately contributing to the development of accurate, patient-specific models in the biomedical domain. |
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