A few-shot identification method for stochastic dynamical systems based on residual multipeaks adaptive sampling.

Neural networks are popular data-driven modeling tools that come with high data collection costs. This paper proposes a residual-based multipeaks adaptive sampling (RMAS) algorithm, which can reduce the demand for a large number of samples in the identification of stochastic dynamical systems. Compared to classical residual-based sampling algorithms, the RMAS algorithm achieves higher system identification accuracy without relying on any hyperparameters. Subsequently, combining the RMAS algorithm and neural network, a few-shot identification (FSI) method for stochastic dynamical systems is proposed, which is applied to the identification of a vegetation biomass change model and the Rayleigh-Van der Pol impact vibration model. We show that the RMAS algorithm modifies residual-based sampling algorithms and, in particular, reduces the system identification error by 76% with the same sample sizes. Moreover, the surrogate model accurately predicts the first escape probability density function and the P bifurcation behavior in the systems, with the error of less than 1.59×10-2. Finally, the robustness of the FSI method is validated.

Entropic stochastic resonance of finite-size particles in confined Brownian transport.

We demonstrate the existence of entropic stochastic resonance (ESR) of passive Brownian particles with finite size in a double- or triple-circular confined cavity, and compare the similarities and differences of ESR in the double-circular cavity and triple-circular cavity. When the diffusion of Brownian particles is constrained to the double- or triple-circular cavity, the presence of irregular boundaries leads to entropic barriers. The interplay between the entropic barriers, a periodic input signal, the gravity of particles, and intrinsic thermal noise may give rise to a peak in the spectral amplification factor and therefore to the appearance of the ESR phenomenon. It is shown that ESR can occur in both a double-circular cavity and a triple-circular cavity, and by adjusting some parameters of the system, the response of the system can be optimized. The differences are that the spectral amplification factor in a triple-circular cavity is significantly larger than that in a double-circular cavity, and compared with the ESR in a double-circular cavity, the ESR effect in a triple-circular cavity occurs within a wider range of external force parameters. In addition, the strength of ESR also depends on the particle radius, and smaller particles can induce more obvious ESR, indicating that the size effect cannot be safely neglected. The ESR phenomenon usually occurs in small-scale systems where confinement and noise play an important role. Therefore, the mechanism that is found could be used to manipulate and control nanodevices and biomolecules.

Tuning Stiffness with Granular Chain Structures for Versatile Soft Robots.

Stiffness variation can greatly enhance soft robots' load capacity and compliance. Jamming methods are widely used where stiffness variation is realized by jamming of particles, layers, or fibers. It is still challenging to make the variable stiffness components lightweight and adaptive. Besides, the existing jamming mechanisms generally encounter deformation-induced softening, restricting their applications in cases where large deformation and high stiffness are both needed. Herein, a multifunctional granular chain assemblage is proposed, where particles are formed into chains with threads. The chain jamming can be classified into two types. Granular chain jamming (GCJ) utilizes typical particles such as spherical particles, which can achieve both high stiffness and great adaptability while keeping jamming components relatively lightweight, while by using cubic particles, a peculiar deformation-induced stiffening mechanism is found, which is termed as stretch-enhanced particle jamming (SPJ). The versatility of GCJ and SPJ mechanisms in soft robots is demonstrated through soft grippers, soft crawlers, or soft bending actuators, where great passive adaptability, high load capacity, joint-like bending, friction enhancement, or postponing buckling can be realized, respectively. This work thus offers a facile and low-cost strategy to fabricate versatile soft robots.

Regularized least absolute deviation-based sparse identification of dynamical systems.

This work develops a regularized least absolute deviation-based sparse identification of dynamics (RLAD-SID) method to address outlier problems in the classical metric-based loss function and the sparsity constraint framework. Our method uses absolute derivation loss as a substitute of Euclidean loss. Moreover, a corresponding computationally efficient optimization algorithm is derived on the basis of the alternating direction method of multipliers due to the non-smoothness of both the new proposed loss function and the regularization term. Numerical experiments are performed to evaluate the effectiveness of RLAD-SID using several exemplary nonlinear dynamical systems, such as the van der Pol equation, the Lorenz system, and the 1D discrete logistic map. Furthermore, detailed numerical comparisons are provided with other existing methods in metric-based sparse regression. Numerical results demonstrate that (1) RLAD-SID shows significant robustness toward a large outlier and (2) RLAD-SID can be seen as a particular metric-based sparse regression strategy that exhibits the effectiveness of the metric-based sparse regression framework for solving outlier problems in a dynamical system identification.

Identical band gaps in structurally re-entrant honeycombs.

Structurally re-entrant honeycomb is a sort of artificial lattice material, characterized by star-like unit cells with re-entrant topology, as well as a high connectivity that the number of folded sheets jointing at each vertex is at least six. In-plane elastic wave propagation in this highly connected honeycomb is investigated through the application of the finite element method in conjunction with the Bloch's theorem. Attention is devoted to exploring the band characteristics of two lattice configurations with different star-like unit cells, defined as structurally square re-entrant honeycomb (SSRH) and structurally hexagonal re-entrant honeycomb (SHRH), respectively. Identical band gaps involving their locations and widths, interestingly, are present in the two considered configurations, attributed to the resonance of the sketch folded sheets, the basic component elements for SSRH and SHRH. In addition, the concept of heuristic models is implemented to elucidate the underlying physics of the identical gaps. The phenomenon of the identical bandgaps is not only beneficial for people to further explore the band characteristics of lattice materials, but also provides the structurally re-entrant honeycombs as potential host structures for the design of lattice-based metamaterials of interest for elastic wave control.

Controlled generation of switching dynamics among metastable states in pulse-coupled oscillator networks.

Switching dynamics among saddles in a network of nonlinear oscillators can be exploited for information encoding and processing (hence computing), but stable attractors in the system can terminate the switching behavior. An effective control strategy is presented to sustain switching dynamics in networks of pulse-coupled oscillators. The support for the switching behavior is a set of saddles, or unstable invariant sets in the phase space. We thus identify saddles with a common property, localize the system in the vicinity of them, and then guide the system from one metastable state to another to generate desired switching dynamics. We demonstrate that the control method successfully generates persistent switching trajectories and prevents the system from entering stable attractors. In addition, there exists correspondence between the network structure and the switching dynamics, providing fundamental insights on the development of a computing paradigm based on the switching dynamics.