Parallel Physics-Informed Neural Networks Method with Regularization Strategies for the Forward-Inverse Problems of the Variable Coefficient Modified KdV Equation

This paper mainly introduces the parallel physics-informed neural networks(PPINNs)method with regularization strategies to solve the data-driven forward-inverse problems of the variable coefficient modified Korteweg-de Vries(VC-MKdV)equation.For the forward problem of the VC-MKdV equation,the authors use the traditional PINN method to obtain satisfactory data-driven soliton solutions and provide a detailed analysis of the impact of network width and depth on solving accuracy and speed.Furthermore,the author finds that the traditional PINN method outperforms the one with locally adaptive activation functions in solving the data-driven forward problems of the VC-MKdV equation.As for the data-driven inverse problem of the VC-MKdV equation,the author introduces a parallel neural networks to separately train the solution function and coefficient function,successfully addressing the function discovery problem of the VC-MKdV equation.To further enhance the network’s generalization ability and noise robustness,the author incorporates two regularization strategies into the PPINNs.An amount of numerical experimental data in this paper demonstrates that the PPINNs method can effectively address the function discovery problem of the VC-MKdV equation,and the inclusion of appropriate regularization strategies in the PPINNs can improves its performance.

A forward-inverse dynamics modeling framework for human musculoskeletal multibody system

Multibody musculoskeletal modeling of human gait has been proved helpful in investigating the pathology of musculoskeletal disorders.However,conventional inverse dynamics methods rely on external force sensors and cannot capture the nonlinear muscle behaviors.Meanwhile,the forward dynamics approach is computationally demanding and only suited for relatively simple tasks.This study proposed an integrated simulation methodology to fulfill the requirements of estimating foot-ground reaction force,tendon elasticity,and muscle recruitment optimization.A hybrid motion capture system,which combines the marker-based infrared device and markerless tracking through deep convolutional neural networks,was developed to track lower limb movements.The foot-ground reaction forces were determined by a contact model for soft materials,and its parameters were estimated using a two-step optimization method.The muscle recruitment problem was first resolved via a static optimization algorithm,and the obtained muscle activations were used as initial values for further simulation.A torque tracking procedure was then performed by minimizing the errors of joint torques calculated by musculotendon equilibrium equations and inverse dynamics.The proposed approach was validated against the electromyography measurements of a healthy subject during gait.The simulation framework provides a robust way of predicting joint torques,musculotendon forces,and muscle activations,which can be beneficial for understanding the biomechanics of normal and pathological gait.