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Temporal data modelling techniques with neural networks are useful in many domain applications, including time-series forecasting and control engineering. This paper aims at developing a recurrent version of stochastic configuration…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
General nonlinear continuous-time systems are considered for which its state is estimated via a packet-based communication network. We assume that the system has multiple sensor nodes, affected by measurement noise, which can transmit at…
Fast and accurate optimization and simulation is widely becoming a necessity for large scale transmission resiliency and planning studies such as N-1 SCOPF, batch contingency solvers, and stochastic power flow. Current commercial tools,…
Many natural and physical processes can be understood by analyzing multiple system variables evolving, forming a multivariate time series. Predicting such time series is challenging due to the inherent noise and interdependencies among…
The increasing integration of distributed energy resources (DERs), variable renewable energy sources, and emerging technologies presents new challenges for transmission system expansion planning (TSEP). Traditional snapshot-based and…
An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the…
Deriving precise system dynamic models through traditional numerical methods is often a challenging endeavor. The performance of Model Predictive Control is heavily contingent on the accuracy of the system dynamic model. Consequently, this…
Modeling the dynamics of the formation and evolution of protostellar disks as well as the history of stellar mass accretion typically involve the numerical solution of complex systems of coupled differential equations. The resulting mass…
We extend the Physics-Informed Echo State Network (PI-ESN) framework to reconstruct the evolution of an unmeasured state (hidden state) in a chaotic system. The PI-ESN is trained by using (i) data, which contains no information on the…
In this work we propose a series-expansion thermal tensor network (SETTN) approach for efficient simulations of quantum lattice models. This continuous-time SETTN method is based on the numerically exact Taylor series expansion of…
In the field of complex dynamics, multistable attractors have been gaining a significant attention due to its unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse…
Many climate processes are characterized using large systems of nonlinear differential equations; this, along with the immense amount of data required to parameterize complex interactions, means that Earth-System Model (ESM) simulations may…
At the heart of time-series forecasting (TSF) lies a fundamental challenge: how can models efficiently and effectively capture long-range temporal dependencies across ever-growing sequences? While deep learning has brought notable progress,…
Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that…
Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…
Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for…
We propose a physics-informed machine learning method to predict the time average of a chaotic attractor. The method is based on the hybrid echo state network (hESN). We assume that the system is ergodic, so the time average is equal to the…
Nonlinear time-history evolution problems employing high-fidelity physical models are essential in numerous scientific domains. However, these problems face a critical dual bottleneck: the immense computational cost of time-stepping and the…
We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean…