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Since many physical laws -- from classical mechanics to electromagnetism -- are formulated as two-body interactions, the same perspective naturally extends to biological and social dynamics. Here we focus on rhythmic phenomena, where phase…
In this paper we propose a framework inspired by interacting particle physics and devised to perform clustering on multidimensional datasets. To this end, any given dataset is modeled as an interacting particle system, under the assumption…
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…
Centuries of development in natural sciences and mathematical modeling provide valuable domain expert knowledge that has yet to be explored for the development of machine learning models. When modeling complex physical systems, both domain…
We develop a robust data fusion algorithm for field reconstruction of multiple physical phenomena. The contribution of this paper is twofold: First, we demonstrate how multi-spatial fields which can have any marginal distributions and…
This paper deals with the problem of adaptive output regulation for multivariable nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. The approach builds on the recently proposed adaptive internal…
The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…
Decades of research in control theory have shown that simple controllers, when provided with timely feedback, can control complex systems. Pushing is an example of a complex mechanical system that is difficult to model accurately due to…
We employ Gaussian process (GP) regression to adjust for systematic errors in D3-type dispersion corrections introducing the associated, statistically improved model D3-GP. We generated a data set containing interaction energies for 1,248…
As we aim to control complex systems, use of a simulator in model-based reinforcement learning is becoming more common. However, it has been challenging to overcome the Reality Gap, which comes from nonlinear model bias and susceptibility…
In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are…
Recent advancements in data-driven aeroelasticity have been driven by the wealth of data available in the wind engineering practice, especially in modeling aerodynamic forces. Despite progress, challenges persist in addressing free-stream…
Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…
It is challenging to perform system identification on soft robots due to their underactuated, high-dimensional dynamics. In this work, we present a data-driven modeling framework, based on geometric mechanics (also known as gauge theory)…
Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…
Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian…
Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of…