Related papers: Dimensional Reduction of Dynamical Systems by Mach…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
In the theory of dynamic programming, an optimal policy is a policy whose lifetime value dominates that of all other policies from every possible initial condition in the state space. This raises a natural question: when does optimality…
We consider the problem of designing almost optimal predictors for dynamical systems from a finite sequence of noisy observations and incomplete knowledge of the dynamics and the noise. We first discuss the properties of the optimal (Bayes)…
The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data -- by distilling underlying principles and mechanisms --…
In this paper, we develop a method to automatically generate a control policy for a dynamical system modeled as a Markov Decision Process (MDP). The control specification is given as a Linear Temporal Logic (LTL) formula over a set of…
Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a…
We predict the emergence of extreme events in a parametrically driven nonlinear dynamical system using three Deep Learning models, namely Multi-Layer Perceptron, Convolutional Neural Network and Long Short-Term Memory. The Deep Learning…
In many real-world decision making problems, reaching an optimal decision requires taking into account a variable number of objects around the agent. Autonomous driving is a domain in which this is especially relevant, since the number of…
This paper studies the problem of dimension reduction, tailored to improving time series forecasting with high-dimensional predictors. We propose a novel Supervised Deep Dynamic Principal component analysis (SDDP) framework that…
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model…
Deep neural networks have become increasingly of interest in dynamical system prediction, but out-of-distribution generalization and long-term stability still remains challenging. In this work, we treat the domain parameters of dynamical…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
This paper considers filtering, parameter estimation, and testing for potentially dynamically misspecified state-space models. When dynamics are misspecified, filtered values of state variables often do not satisfy model restrictions,…
Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model…
One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
With the rapid development of more complex robots, Fault Detection and Diagnosis (FDD) becomes increasingly harder. Especially the need for predetermined models and historic data is problematic because they do not encompass the dynamic and…
One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…
Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…
We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that…