[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82213-en":3,"doc-seo-82213-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82213,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Residual Physics-Informed Neural Networks for High-Fidelity BLDC Motor Modeling","Accurate dynamics modeling of Brushless DC (BLDC) motors underpins high-performance robotic joint control. The work introduces a physics-informed neural network (PINN) with a deep residual (ResNet) backbone that learns a continuous-time surrogate of the full six-state BLDC dynamics. Inputs include simulation time, three-phase voltages, and excitation parameters; outputs directly predict rotor angle, angular velocity, phase currents, and winding temperature while enforcing electromechanical and thermal ODEs via a composite physics-data loss. Curriculum scheduling activates physics penalties gradually to avoid early training collapse. Training completes under two minutes on a CPU, and inference achieves 0.1–22 μs latency per query, enabling real-time observer/control use and providing up to 118× speedup over conventional ODE solvers.","Residual Physics-Informed Neural Networks for High-Fidelity BLDC Motor Modeling  \nHaitham El-Hussieny  \nDepartment of Mechatronics and Robotics Engineering,  \nEgypt-Japan University of Science and Technology (E-JUST),  \nNew Burg El-Arab City, Alexandria, Egypt  \n[haitham.elhussieny@ejust.edu.eg](haitham.elhussieny@ejust.edu.eg)  \narXiv :2607 .09136v1 [ cs .RO] 10 Jul 2026  \nAbstract—Accurate dynamics modeling of Brushless DC (BLDC) motors is fundamental to high-performance robotic joint control. This paper presents a Physics-Informed Neural Network (PINN) with a deep residual (ResNet) backbone that learns a continuous-time surrogate of the full six-state BLDC motor dynamics. Given simulation time, applied three-phase voltages, and excitation parameters as inputs, the network directly predicts all motor state variables—rotor angle, angular velocity, threephase currents, and winding temperature—while simultaneously satisfying the governing electromechanical and thermal ODEs through a composite physics-data loss. A curriculum scheduling strategy gradually activates the physics penalty to prevent premature convergence. Training runs are completed in under two minutes on a standard CPU. Crucially, once trained, PINN inference achieves latencies of 0. 1–22µs per query, up to 118 × faster than conventional ODE solvers, making it suitable for realtime observer and control applications.  \nIndex Terms—Brushless DC motor, physics-informed neural network, ResNet, residual architecture, surrogate modeling, ODE residual, curriculum learning, model latency, real-time inference.  \nI. INTRODUCTION  \nBrushless DC motors are the actuators of choice in modern legged robots, aerial vehicles, and collaborative manipulatorsowing to their high torque-to-weight ratio, efficiency, and controllability [1] . Model-based control strategies—feedforward linearisation, sliding mode, iterative learning control, and model-predictive control [7], [8]—depend critically on accurate, computationally cheap dynamics models. Classical white-box models derived from first-principles ODEs are interpretable but require precise parameter identification; even small errors in resistance or inductance propagate into significant control degradation. Conversely, black-box neural networks can approximate complex mappings but tend to violate physical laws outside the training distribution.  \nPhysics-Informed Neural Networks (PINNs), introduced by Raissi et al. [2], embed differential-equation residuals directly into the training loss, bridging data-fitting accuracy with physical interpretability. Their success spans heat transfer [3], fluid dynamics, and structural health monitoring.  \nApplication to electric motor dynamics, however, remains nascent. Recent expansions into multiphysics-informed neural networks (MPINNs) highlight their capacity to handle complex mechatronic configurations—such as electric motor thermalelectromechanical interactions—by embedding coupled scien-  \ntific domain principles straight into the network layers [9] . Nevertheless, standard fully-connected PINNs suffer from vanishing gradients and spectral bias when stacked deeply...  \nStandard fully-connected PINNs suffer from vanishing gradients and spectral bias when stacked deeply [5] . Residual connections, popularised by He et al. [4] for image recognition, guarantee unit-norm gradient propagation at initialisation and have been shown to accelerate PINN convergence on stiff ODEs.  \nA critical but often overlooked practical requirement is inference speed: a surrogate model deployed inside a real-time controller or state estimator must respond within the control period (typically \u003C 1ms) . Numerical ODE solvers cannot easily meet this requirement at high accuracy.  \nThis paper makes the following contributions:  \n• A continuous-time ResNet-PINN surrogate for a threephase BLDC motor mapping (t, f, A, Va , Vb , Vc) to the full six-dimensional state [θ,ω, Ia , Ib , Ic , T], with properly computed autograd ph","cbCaifTZ22BRRSvD","https://ap.wps.com/l/cbCaifTZ22BRRSvD","pdf",979704,1,5,"English","en",105,"# Introduction\n# BLDC Motor Model\n## Motor Description\n## Governing Equations","[{\"question\":\"What does the proposed ResNet-PINN model predict for a BLDC motor?\",\"answer\":\"Given time, three-phase voltages, and excitation parameters, it predicts rotor angle, angular velocity, three phase currents, and winding temperature as a continuous-time surrogate of the full six-state dynamics.\"},{\"question\":\"How does the method enforce physical consistency during training?\",\"answer\":\"It uses a composite physics-data loss that embeds residuals of the electromechanical and thermal ODEs computed through automatic differentiation, tying network outputs to governing differential equations.\"},{\"question\":\"Why is curriculum scheduling used in this PINN approach?\",\"answer\":\"Curriculum scheduling gradually activates the physics penalty, preventing premature convergence and allowing the network to fit data first before stronger equation constraints are 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does the proposed ResNet-PINN model predict for a BLDC motor?","Question",{"text":75,"@type":76},"Given time, three-phase voltages, and excitation parameters, it predicts rotor angle, angular velocity, three phase currents, and winding temperature as a continuous-time surrogate of the full six-state dynamics.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method enforce physical consistency during training?",{"text":80,"@type":76},"It uses a composite physics-data loss that embeds residuals of the electromechanical and thermal ODEs computed through automatic differentiation, tying network outputs to governing differential equations.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is curriculum scheduling used in this PINN approach?",{"text":84,"@type":76},"Curriculum scheduling gradually activates the physics penalty, preventing premature convergence and allowing the network to fit data first before stronger equation constraints are 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