Flow control and sensing using data-driven reduced-order modeling

Transfer operators, such as the Koopman operator, are driving a paradigm shift in how we perform data-driven modeling of fluid flows. Approximations of the Koopman operator provide linear representations even for strongly nonlinear flows, which enables the application of standard linear methods for estimation and control under realistic flow conditions. In the past decade, we have witnessed several breakthroughs in obtaining low-dimensional approximations of the Koopman operators, providing a tractable reduced-order model for complex fluid flows using data from numerical simulations or experiments. In this thesis, we leverage these recent developments in operator-theoretic modeling of fluid flows and provide data-driven solutions to the flow control and sensing problems. The contributions of this thesis can be divided into three parts. In the first part, we introduce a novel method, low-rank Dynamic Mode Decomposition (lrDMD), for data-driven reduced-order modeling of fluid flows. While existing data-driven modeling methods fit an endomorphic linear function on a low-dimensional subspace, lrDMD approximates flow dynamics using a linear map between different subspaces. We show that this approach leads to the design of better reduced-order feedback controllers. We formulate a rank-constrained matrix optimization problem and propose two complementary methods to solve the problem. lrDMD outperforms existing methods in feedback control and optimal actuator placement. In the second part, we present a completely data-driven framework for sensor placement in fluid flows. This framework can be applied in conjunction with any reduced-order modeling technique that constructs a linear model for the flow dynamics. We formulate an optimization problem that minimizes the trace of a data-driven approximation of the estimation error covariance matrix, where the estimates are provided by a Kalman filter. We propose an efficient adjoint-based gradient descent method to solve the optimization problem. We show that sensors placed using our method lead to better performance in important applications, such as flow estimation and control, compared to existing data-driven sensor placement methods. In the third and final part, we propose a new method of interface tracking and reconstruction in multiphase flows using shadowgraphs or back-lit imaging data. First, we show that while traditional modeling methods provide valuable information about the spatio-temporal structure of flow instabilities, they are not able to resolve spatial or temporal discontinuities, such as the liquid-gas interface, in the data. To remedy this, we propose a two-step approach, using data-driven modeling techniques in conjunction with optical flow methods, that preserves sharp interfaces and provides reliable reconstruction and short-time prediction of the flow. We apply our method to an experimental liquid jet with a co-axial air-blast atomizer using back-lit imaging. Our method is able to accurately reconstruct and predict the flow while preserving the sharpness of the liquid-gas interface

Parsimonious Clone Tree Integration in cancer

BACKGROUND: Every tumor is composed of heterogeneous clones, each corresponding to a distinct subpopulation of cells that accumulated different types of somatic mutations, ranging from single-nucleotide variants (SNVs) to copy-number aberrations (CNAs). As the analysis of this intra-tumor heterogeneity has important clinical applications, several computational methods have been introduced to identify clones from DNA sequencing data. However, due to technological and methodological limitations, current analyses are restricted to identifying tumor clones only based on either SNVs or CNAs, preventing a comprehensive characterization of a tumor's clonal composition. RESULTS: To overcome these challenges, we formulate the identification of clones in terms of both SNVs and CNAs as a integration problem while accounting for uncertainty in the input SNV and CNA proportions. We thus characterize the computational complexity of this problem and we introduce PACTION (PArsimonious Clone Tree integratION), an algorithm that solves the problem using a mixed integer linear programming formulation. On simulated data, we show that tumor clones can be identified reliably, especially when further taking into account the ancestral relationships that can be inferred from the input SNVs and CNAs. On 49 tumor samples from 10 prostate cancer patients, our integration approach provides a higher resolution view of tumor evolution than previous studies. CONCLUSION: PACTION is an accurate and fast method that reconstructs clonal architecture of cancer tumors by integrating SNV and CNA clones inferred using existing methods

Parsimonious Clone Tree Reconciliation in Cancer

Every tumor is composed of heterogeneous clones, each corresponding to a distinct subpopulation of cells that accumulated different types of somatic mutations, ranging from single-nucleotide variants (SNVs) to copy-number aberrations (CNAs). As the analysis of this intra-tumor heterogeneity has important clinical applications, several computational methods have been introduced to identify clones from DNA sequencing data. However, due to technological and methodological limitations, current analyses are restricted to identifying tumor clones only based on either SNVs or CNAs, preventing a comprehensive characterization of a tumor's clonal composition. To overcome these challenges, we formulate the identification of clones in terms of both SNVs and CNAs as a reconciliation problem while accounting for uncertainty in the input SNV and CNA proportions. We thus characterize the computational complexity of this problem and we introduce a mixed integer linear programming formulation to solve it exactly. On simulated data, we show that tumor clones can be identified reliably, especially when further taking into account the ancestral relationships that can be inferred from the input SNVs and CNAs. On 49 tumor samples from 10 prostate cancer patients, our reconciliation approach provides a higher resolution view of tumor evolution than previous studies