Related papers: Model order reduction of deep structured state-spa…
Common trends in model order reduction of large nonlinear finite-element-discretized systems involve the introduction of a linear mapping into a reduced set of unknowns, followed by Galerkin projection of the governing equations onto a…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
In this paper, we bring together the worlds of model order reduction for stochastic linear systems and $\mathcal H_2$-optimal model order reduction for deterministic systems. In particular, we supplement and complete the theory of error…
In energy-efficient schemes, finding the optimal size of deep learning models is very important and has a broad impact. Meanwhile, recent studies have reported an unexpected phenomenon, the sparse double descent: as the model's sparsity…
A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around…
For many practical computer vision applications, the learned models usually have high performance on the datasets used for training but suffer from significant performance degradation when deployed in new environments, where there are…
In the quest for next-generation sequence modeling architectures, State Space Models (SSMs) have emerged as a potent alternative to transformers, particularly for their computational efficiency and suitability for dynamical systems. This…
Simulations of large scale dynamical systems in multi-query or real-time contexts require efficient surrogate modelling techniques, as e.g. achieved via Model Order Reduction (MOR). Recently, symplectic methods like the complex singular…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…
Structural causal models (SCMs) are a powerful tool for understanding the complex causal relationships that underlie many real-world systems. As these systems grow in size, the number of variables and complexity of interactions between them…
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the…
The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns…
The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…
Despite their successes, deep learning models struggle with tasks requiring complex reasoning and function composition. We present a theoretical and empirical investigation into the limitations of Structured State Space Models (SSMs) and…
The manipulator workspace mapping is an important problem in robotics and has attracted significant attention in the community. However, most of the pre-existing algorithms have expensive time complexity due to the reliance on sophisticated…
This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus…
In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method…