Related papers: Practical challenges in data-driven interpolation:…

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…

This paper deals with the problem of providing a data-driven solution to the local stabilization of linear systems subject to input saturation. After presenting a model-based solution to this well-studied problem, a systematic method to…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

With the advantages of high modeling accuracy and large bandwidth, recurrent neural network (RNN) based inversion model control has been proposed for output tracking. However, some issues still need to be addressed when using the RNN-based…

In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…

This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of…

This article develops a novel data assimilation methodology, addressing challenges that are common in real-world settings, such as severe sparsity of observations, lack of reliable models, and non-stationarity of the system dynamics. These…

Pulse stabilization of cycles with Prediction-Based Control including noise and stochastic stabilization of maps with multiple equilibrium points is analyzed for continuous but, generally, non-smooth maps. Sufficient conditions of global…

Sound synthesizers are widespread in modern music production but they increasingly require expert skills to be mastered. This work focuses on interpolation between presets, i.e., sets of values of all sound synthesis parameters, to enable…

Standard tabular benchmarks mainly focus on the evaluation of a model's capability to interpolate values inside a data manifold, where models good at performing local statistical smoothing are rewarded. However, there exists a very large…

Noise is one of the primary sources of interference in seismic exploration. Many authors have proposed various methods to remove noise from seismic data; however, in the face of strong noise conditions, satisfactory results are often not…

This work proposes a robust data-driven predictive control approach for unknown nonlinear systems in the presence of bounded process and measurement noise. Data-driven reachable sets are employed for the controller design instead of using…

We propose a data-driven interpolation method for approximating real-valued functions on smooth manifolds, based on the Laplace--Beltrami operator and Voronoi tessellations. Given pointwise evaluations, the method constructs a continuous…

In the recent years, we have observed three significant trends in control systems: a renewed interest in data-driven control design, the abundance of cloud computational services and the importance of preserving privacy for the system under…

Thanks to novel, powerful brain activity recording techniques, we can create data-driven models from thousands of recording channels and large portions of the cortex, which can improve our understanding of brain-states neuromodulation and…

In this note, we explore a middle ground between data-driven model reduction and data-driven control. In particular, we use snapshots collected from the system to build reduced models that can be expressed in terms of data. We illustrate…

Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using…

One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…

This paper introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound…