Related papers: Sparse learning of stochastic dynamic equations
Extrapolative prediction of complex nonlinear dynamics remains a central challenge in engineering. This study proposes a one-shot learning method to identify global frequency-response curves from a single excitation time history by learning…
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…
Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space…
In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the…
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…
Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional…
Complex systems in physics, chemistry, and biology that evolve over time with inherent randomness are typically described by stochastic differential equations (SDEs). A fundamental challenge in science and engineering is to determine the…
Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…
We develop data-driven dynamical models of the nonlinear aeroelastic effects on a long-span suspension bridge from sparse, noisy sensor measurements which monitor the bridge. Using the {\em sparse identification of nonlinear dynamics}…
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…
Air pollution, particularly particulate matter (PM2.5), poses significant risks to public health and the environment, necessitating accurate prediction and continuous monitoring for effective air quality management. However, air quality…
This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the…
Research on dynamics of robotic manipulators provides promising support for model-based control. In general, rigorous first-principles-based dynamics modeling and accurate identification of mechanism parameters are critical to achieving…
To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…
In future power systems, the detailed structure and dynamics may not always be fully known. This is due to an increasing number of distributed energy resources, such as photovoltaic generators, battery storage systems, heat pumps and…
Inferring physical laws from data is a central challenge in science and engineering, including but not limited to healthcare, physical sciences, biosciences, social sciences, sustainability, climate, and robotics. Deep networks offer…
We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…