Related papers: Dissipative Deep Neural Dynamical Systems

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

We investigate the dissipative dynamics of linear and nonlinear waves in harmonic traps by means of engineered complex non-Hermitian potentials. By combining an analytical mapping between real and complex Schr\"odinger equations with direct…

The simulation of driven dissipative quantum dynamics is often prohibitively computation-intensive, especially when it is calculated for various shapes of the driving field. We engineer a new feature space for representing the field and…

Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…

This paper deals with differentiable dynamical models congruent with neural process theories that cast brain function as the hierarchical refinement of an internal generative model explaining observations. Our work extends existing…

We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

This paper studies the problem of verifying dissipativity of linear time-invariant (LTI) systems using input-output data. We leverage behavioral systems theory to express dissipativity in terms of quadratic difference forms (QDFs), allowing…

This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces. A general framework is established in which the value function and continuation…

When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction, and…

In this communication we demonstrate that a deep artificial neural network based on a transformer architecture with self-attention layers can predict the long-time population dynamics of a quantum system coupled to a dissipative environment…

Two major uncertainties, dataset bias and adversarial examples, prevail in state-of-the-art AI algorithms with deep neural networks. In this paper, we present an intuitive explanation for these issues as well as an interpretation of the…

We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition (DMD) on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this…

This paper explores the use of deep neural networks for semiparametric estimation of economic models of maximizing behavior in production or discrete choice. We argue that certain deep networks are particularly well suited as a…

The paper is considered with the dissipative theory and feedback control under the framework of dissipation with the supply rate is the inner product of input u and the derivation of output y for the linear/nonlinear time-invariant input…

We introduce dissipative spectroscopy as a framework for extracting spectral information from quantum systems via controlled dissipation. By establishing a general dissipative response theory applicable to both Markovian and non-Markovian…

Conservation of energy is at the core of many physical phenomena and dynamical systems. There have been a significant number of works in the past few years aimed at predicting the trajectory of motion of dynamical systems using neural…

Neural networks have become a widely adopted tool for tackling a variety of problems in machine learning and artificial intelligence. In this contribution we use the mathematical framework of local stability analysis to gain a deeper…

In a physical neural system, where storage and processing are intimately intertwined, the rules for adjusting the synaptic weights can only depend on variables that are available locally, such as the activity of the pre- and post-synaptic…

The dynamics of affective decision making is considered for an intelligent network composed of agents with different types of memory: long-term and short-term memory. The consideration is based on probabilistic affective decision theory,…