Related papers: Predictive Dynamical Systems
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
Identifying and understanding modular organizations is centrally important in the study of complex systems. Several approaches to this problem have been advanced, many framed in information-theoretic terms. Our treatment starts from the…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
A clear definition of system dynamics modeling can provide shared understanding and clarify the impact of the field. We introduce a set of characteristics that define quantitative system dynamics, selected to capture core philosophy,…
Accurately predicting the dynamics of robotic systems is crucial for model-based control and reinforcement learning. The most common way to estimate dynamics is by fitting a one-step ahead prediction model and using it to recursively…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
We introduce a method for learning the dynamics of complex nonlinear systems based on deep generative models over temporal segments of states and actions. Unlike dynamics models that operate over individual discrete timesteps, we learn the…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
Deterministic many-body systems governed by simple interactions can self-organize into macroscopic patterns, and the determinants of long-time behavior are assumed to be encoded in the initial configuration. Here we show that predictability…
Modern learning systems increasingly interact with data that evolve over time and depend on hidden internal state. We ask a basic question: when is such a dynamical system learnable from observations alone? This paper proposes a research…
Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…
Uncertainty plays a key role in future prediction. The future is uncertain. That means there might be many possible futures. A future prediction method should cover the whole possibilities to be robust. In autonomous driving, covering…
The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…
We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
A general scheme for construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…
Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant…