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Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
Topological Data Analysis (TDA) has been praised by researchers for its ability to capture intricate shapes and structures within data. TDA is considered robust in handling noisy and high-dimensional datasets, and its interpretability is…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
Data-driven predictive control approaches, in general, and Data-enabled Predictive Control (DeePC), in particular, exploit matrices of raw input/output trajectories for control design. These data are typically gathered only from the system…
In this paper, we address a general eigenstructure assignment problem where the objective is to distribute the closed-loop modes over the components of the system outputs in such a way that, if a certain mode appears in a given output, it…
In this paper, we consider networked systems comprised of interconnected sets of linear subsystems and propose a decentralized and compositional approach to stabilize or dissipativate such linear networked systems via optimally modifying…
A transformed auto-correlation method is presented here, where a received signal is transformed based on a priori reflecting model, and then the transformed signal is cross-correlated to its original one. If the model is correct, after…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Deep neural networks (DNNs) deliver outstanding performance, but their complexity often prohibits deployment in resource-constrained settings. Comprehensive structured pruning frameworks based on parameter dependency analysis reduce model…
In recent years, machine learning models have been increasingly applied to spectroscopic datasets for chemical and biomedical analysis. For their successful adoption, particularly in clinical and safety-critical settings, professionals and…
In \emph{Guo et al, arXiv:2005.08288}, we propose a decoupled form of the structure-preserving doubling algorithm (dSDA). The method decouples the original two to four coupled recursions, enabling it to solve large-scale algebraic Riccati…
Many correct-by-construction control synthesis methods suffer from the curse of dimensionality. Motivated by this challenge, we seek to reduce a correct-by-construction control synthesis problem to subproblems of more modest dimension. As a…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…
Link prediction is a crucial task in graph machine learning with diverse applications. We explore the interplay between node attributes and graph topology and demonstrate that incorporating pre-trained node attributes improves the…
In the context of MDPs with high-dimensional states, downstream tasks are predominantly applied on a compressed, low-dimensional representation of the original input space. A variety of learning objectives have therefore been used to attain…
This paper proposes a form of MPC in which the control variables are moved asynchronously. This contrasts with most MIMO control schemes, which assume that all variables are updated simultaneously. MPC outperforms other control strategies…