Related papers: Balance-Guided Sparse Identification of Multiscale…
Quantum feature maps offer expressive embeddings for classical learning tasks, and augmenting sparse identification of nonlinear dynamics (SINDy) with such features is a natural but unexplored direction. We introduce \textbf{Q-SINDy}, a…
Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on…
Extracting governing equations from dynamic data is an essential task in model selection and parameter estimation. The form of the governing equation is rarely known a priori; however, based on the sparsity-of-effect principle one may…
This study proposes a novel framework for learning the underlying physics of phenomena with moving boundaries. The proposed approach combines Ensemble SINDy and Peridynamic Differential Operator (PDDO) and imposes an inductive bias assuming…
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
In the study of complex dynamical systems, understanding and accurately modeling the underlying physical processes is crucial for predicting system behavior and designing effective interventions. Yet real-world systems exhibit pronounced…
Compressed sensing is an important problem in many fields of science and engineering. It reconstructs signals by finding sparse solutions to underdetermined linear equations. In this work we propose a deterministic and non-parametric…
This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same…
We propose a sequential learning policy for noisy discrete global optimization and ranking and selection (R\&S) problems with high dimensional sparse belief functions, where there are hundreds or even thousands of features, but only a small…
Power grid parameter estimation involves the estimation of unknown parameters, such as inertia and damping coefficients, using observed dynamics. In this work, we present a comparison of data-driven algorithms for the power grid parameter…
Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense…
This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from noisy data using a combination of sparse regression and weak formulation. Using the…
We propose a novel data-driven method called QENDy (Quadratic Embedding of Nonlinear Dynamics) that not only allows us to learn quadratic representations of highly nonlinear dynamical systems, but also to identify the governing equations.…
Predicting the human burden of vector-borne diseases from limited surveillance data remains a major challenge, particularly in the presence of nonlinear transmission dynamics and delayed effects arising from vector ecology and human…
This paper deals with the error processing problem of sparse identification of nonlinear dynamical systems(SINDy) through introducing the $L_\infty$ approximation to take place of the former $L_2$ approximation. The motivation is that the…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
Supervised learning under measurement constraints is a common challenge in statistical and machine learning. In many applications, despite extensive design points, acquiring responses for all points is often impractical due to resource…
Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse…