Related papers: Data-driven identification of stable differential …

In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…

This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are…

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…

Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. There is an emerging literature on tackling this problem by…

Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably…

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders,…

We propose a two-step procedure to detect cointegration in high-dimensional settings, focusing on sparse relationships. First, we use the adaptive LASSO to identify the small subset of integrated covariates driving the equilibrium…

Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…

We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy…

The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained…

We develop a new framework for learning variational autoencoders and other deep generative models that balances generative and discriminative goals. Our framework optimizes model parameters to maximize a variational lower bound on the…

This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…

Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…

Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. Recently, there are robust learning methods aiming at this…

Finding the governing equations from data by sparse optimization has become a popular approach to deterministic modeling of dynamical systems. Considering the physical situations where the data can be imperfect due to disturbances and…

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and…

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…