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In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…
This paper proposes a state reduction method for learning-based model predictive control (MPC) for train rescheduling in urban rail transit systems. The state reduction integrates into a control framework where the discrete decision…
Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Variational formulations of time-dependent PDEs in space and time yield $(d+1)$-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables…
Linear Parameter-Varying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far. We fill this gap…
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…
In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our…
This paper develops an adaptive state tracking control scheme for discrete-time systems, using the least-squares algorithm, as the new solution to the long-standing discrete-time adaptive state tracking control problem to which the Lyapunov…
This work aims at tackling the problem of learning surrogate models from noisy time-domain data by means of matrix pencil-based techniques, namely the Hankel and Loewner frameworks. A data-driven approach to obtain reduced-order state-space…
We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
A state-space representation of water quality dynamics describing disinfectant (e.g., chlorine) transport dynamics in drinking water distribution networks has been recently proposed. Such representation is a byproduct of space- and…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
Aligning Large Language Models (LLM) to address subjectivity and nuanced preference levels requires adequate flexibility and control, which can be a resource-intensive and time-consuming procedure. Existing training-time alignment methods…
Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…
We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…
We propose a general dynamic reduced-order modeling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved PIV snapshots. This framework contains four steps. First, the sensor signals are lifted to…