Related papers: Data-driven discovery of partial differential equa…

This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by…

With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…

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…

In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…

This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Discovering explicit governing equations of stochastic dynamical systems with both (Gaussian) Brownian noise and (non-Gaussian) L\'evy noise from data is chanllenging due to possible intricate functional forms and the inherent complexity of…

In this paper, an evolutionary-based sparse regression algorithm is proposed and applied onto experimental data collected from a Duffing oscillator setup and numerical simulation data. Our purpose is to identify the Coulomb friction terms…

In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…

A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…

Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

Physics-informed methods have gained a great success in analyzing data with partial differential equation (PDE) constraints, which are ubiquitous when modeling dynamical systems. Different from the common penalty-based approach, this work…

State estimation is required whenever we deal with high-dimensional dynamical systems, as the complete measurement is often unavailable. It is key to gaining insight, performing control or optimizing design tasks. Most deep learning-based…

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

In this work we propose a novel approach for modeling spatio-temporal data characterized by group structures. In particular, we extend classical mixed effect regression models by introducing a space-time nonparametric component, regularized…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of…

The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic…

Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…