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In this paper, we propose a very efficient numerical method based on the L-BFGS-B algorithm for identifying linear and nonlinear discrete-time state-space models, possibly under $\ell_1$ and group-Lasso regularization for reducing model…
Nudging is an empirical data assimilation technique that incorporates an observation-driven control term into the model dynamics. The trajectory of the nudged system approaches the true system trajectory over time, even when the initial…
The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i)…
Recurrent neural networks (RNNs) are a vital modeling technique that rely on internal states learned indirectly by optimization of a supervised, unsupervised, or reinforcement training loss. RNNs are used to model dynamic processes that are…
Real-time traffic prediction from high-fidelity spatiotemporal traffic sensor datasets is an important problem for intelligent transportation systems and sustainability. However, it is challenging due to the complex topological dependencies…
The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
In this paper, we study the "stability" of machine learning (ML) models within the context of larger, complex NLP systems with continuous training data updates. For this study, we propose a methodology for the assessment of model stability…
We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop…
This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…
This paper presents a robust control synthesis and analysis framework for nonlinear systems with uncertain initial conditions. First, a deep learning-based lifting approach is proposed to approximate nonlinear dynamical systems with linear…
We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
Nonlinear vector autoregression (NVAR) and reservoir computing (RC) have shown promise in forecasting chaotic dynamical systems, such as the Lorenz-63 model and El Nino-Southern Oscillation. However, their reliance on fixed nonlinear…
This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of…
Time series forecasting based on deep architectures has been gaining popularity in recent years due to their ability to model complex non-linear temporal dynamics. The recurrent neural network is one such model capable of handling…
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…
Short-term traffic forecasting based on deep learning methods, especially recurrent neural networks (RNN), has received much attention in recent years. However, the potential of RNN-based models in traffic forecasting has not yet been fully…
The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e. physics based) or data-driven (i.e. machine-learning based) origins. In order to combine the strengths of these two…