Purpose of review: In this review, we briefly summarize the numerical methods commonly used for the nonlinear dynamic analysis of soft robotic systems. The underlying mechanical principles as well as the geometrical treatment tailored for soft robots are introduced with particular emphasis on one-dimensional models. Additionally, the review encompasses three-dimensional frameworks, available simulation packages, and various types of interaction models, shedding light on the design, actuation, motion control, and internal and external forces of soft robots. Recent findings: Reduced-order models can offer high efficiency in characterizing nonlinear deformations, allowing convenient tailoring based on specific structural and material configurations. For pursuing high simulation accuracy and detailed mechanics, the finite element method proves to be a valuable tool through numerous off-the-shelf platforms. Furthermore, machine learning has emerged as a promising tool to effectively address the challenges within the mechanics community. Summary: A wide range of kinematic and dynamic numerical models is available for simulating the behaviors of soft robots, offering exceptional adaptability to different geometries and structures based on existing modeling theories and numerical solution algorithms. However, the trade-off between computational complexity and simulation accuracy remains a challenge in achieving fast, accurate, and robust control of soft robots in complex environments.

Artificial neural network (ANN) was proposed as an effective method to help multipath ultrasonic flowmeter (UFM) reduce its measurement error when determining the flowrate of complex flow field. However, the effectiveness of the ANN method heavily depends on the network architecture specified by the designer, and also the provided initial weights and layer biases. This hinders the ANN to be widely used in actual UFMs. This paper proposes a genetic algorithm (GA) optimized ANN method (GANN) to be used in UFMs. The GA is utilized to determine ANN architecture based on its efficient parallel advantage in global search to replace traditional trial and error approach or empirical method. In addition, the initial weights and biases are optimized by GA, which is capable to avoid the network getting stuck with local minimum and qualify it for good generalization ability. Tests are implemented on numerical models simulating a six-path UFM installed downstream single or double elbows with complex flow field passing through it. Comparisons between the results of classical Gaussian quadrature, existing ANN, and proposed GANN are given for verification. The flowrate determination error of GANN is only 40% ~ 62% of existing ANN, which is extremely smaller than the Gaussian quadrature method. In addition, the output of GANN is much more stable than existing ANN, as proper initial weights and layer biases will be generated by GA for iteration process even random data are given for training.