Related papers: Transport in reservoir computing
We investigate the dynamics of the driven open double two-level system by deriving a driven Markovian master equation based on the Lewis-Riesenfeld invariant theory. The transitions induced by coupling to the heat reservoir occur between…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic…
This paper focuses on the performance and the robustness analysis of stochastic jump linear systems. The state trajectory under stochastic jump process becomes random variables, which brings forth the probability distributions in the system…
The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. Initial lack of knowledge of the system and external noises are accounted…
The determination of the conductivity of a deterministic or stochastic classical system coupled to reservoirs at its ends can in general be mapped onto the problem of computing the stiffness (the `energy' cost of twisting the boundaries) of…
We present theory and algorithms for the computation of probability-weighted "keep-out" sets to assure probabilistically safe navigation in the presence of multiple rigid body obstacles with stochastic dynamics. Our forward stochastic…
In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide…
Reservoir Computing offers a great computational framework where a physical system can directly be used as computational substrate. Typically a "reservoir" is comprised of a large number of dynamical systems, and is consequently…
Reservoir Computing (RC) with physical systems requires an understanding of the underlying structure and internal dynamics of the specific physical reservoir. In this study, physical nano-electronic networks with neuromorphic dynamics are…
We study the paradigmatic model of a qubit interacting with a structured environment and driven by an external field by means of a microscopic and a phenomenological model. The validity of the so-called fixed-dissipator (FD) assumption,…
This paper introduces a methodology for identifying and simulating financial and economic systems using stochastically structured reservoir computers (SSRCs). The framework combines structure-preserving embeddings with graph-informed…
The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each…
Reservoir Computing is a novel computing paradigm which uses a nonlinear recurrent dynamical system to carry out information processing. Recent electronic and optoelectronic Reservoir Computers based on an architecture with a single…
A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…
For a reservoir computer composed of a single nonlinear node and delay line, we show that after a finite period of discrete time, the distance between two reservoir outputs is bounded above by a constant multiple of the distance between…
We extend flow matching to ensembles of linear systems in both deterministic and stochastic settings. Averaging over system parameters induces memory leading to a non-Markovian interpolation problem for the stochastic case. In this setting,…
Reservoir computing has proven effective for tasks such as time-series prediction, particularly in the context of chaotic systems. However, conventional reservoir computing frameworks often face challenges in achieving high prediction…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
We formulate, using the discrete nonlinear Schroedinger equation (DNLS), a general approach to encode and process information based on reservoir computing. Reservoir computing is a promising avenue for realizing neuromorphic computing…