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Nonlocal models have recently had a major impact in nonlinear continuum mechanics and are used to describe physical systems/processes which cannot be accurately described by classical, calculus based "local" approaches. In part, this is due…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
The complex eigenvalues of Markov generators govern oscillatory properties of relaxation, autocorrelation, and linear response. Here we show that these eigenvalues are localized by nonequilibrium cycles of the generator, thus revealing a…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…
Periodic recurrence is a prominent behavioural of many biological phenomena, including cell cycle and circadian rhythms. Although deterministic models are commonly used to represent the dynamics of periodic phenomena, it is known that they…
We derive optimal periodic controls for entrainment of a self-driven oscillator to a desired frequency. The alternative objectives of minimizing power and maximizing frequency range of entrainment are considered. A state space…
The optimization of physical parameters serves various purposes, such as system identification and efficiency in developing devices. Spin-torque oscillators have been applied to neuromorphic computing experimentally and theoretically, but…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…
Multi-body mechanical systems have rich internal dynamics, whose solutions can be exploited as efficient control targets. Yet, solutions non-trivially depend on system parameters, obscuring feasible properties for use as target…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
Human movement prediction is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose a prediction framework that decouples short-term…
We develop the theory of Energy Conserving Descent (ECD) and introduce ECDSep, a gradient-based optimization algorithm able to tackle convex and non-convex optimization problems. The method is based on the novel ECD framework of…
For oscillating time series, the prediction is often focused on the turning points. In order to predict the turning point magnitudes and times it is proposed to form the state space reconstruction only from the turning points and modify the…
Recurrent Neural Networks (RNNs) have found widespread applications in machine learning for time series prediction and dynamical systems reconstruction, and experienced a recent renaissance with improved training algorithms and…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
Computation, mechanics and materials merge in biological systems, which can continually self-optimize through internal adaptivity across length scales, from cytoplasm and biofilms to animal herds. Recent interest in such material-based…
Computing gradients of a cost function is central to design-based optimization and machine learning algorithms. Equilibrium propagation provides an exact method to compute gradients in hardware by exploiting the inherent physical laws. The…
An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments,…