Related papers: Ordinary Differential Equation-based Sparse Signal…
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in…
Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…
Lasso problems arise in many areas, including signal processing, machine learning, and control, and are closely connected to sparse coding mechanisms observed in neuroscience. A continuous-time ordinary differential equation (ODE)…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…
An approximate sparse recovery system in ell_1 norm formally consists of parameters N, k, epsilon an m-by-N measurement matrix, Phi, and a decoding algorithm, D. Given a vector, x, where x_k denotes the optimal k-term approximation to x,…
We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
Learning dynamical systems is a promising avenue for scientific discoveries. However, capturing the governing dynamics in multiple environments still remains a challenge: model-based approaches rely on the fidelity of assumptions made for a…
Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence.…
Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these…
In this paper, we study ordinary differential equations (ODE) coupled with solutions of a stochastic nonsmooth convex optimization problem (SNCOP). We use the regularization approach, the sample average approximation and the time-stepping…
This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…
In this paper, we consider the problem of collaboratively estimating the sparsity pattern of a sparse signal with multiple measurement data in distributed networks. We assume that each node makes Compressive Sensing (CS) based measurements…