Parallelizable Complex Neural Dynamics Models for PMSM Temperature Estimation with Hardware Acceleration

TL;DR

The paper tackles the challenge of real-time, accurate PMSM temperature estimation by introducing a physics-informed, hardware-efficient complex neural dynamics model (complexNDM) built on diagonalizable state-space representations. It embeds stability and oscillation priors in the complex domain, enforces a smooth evolution of hidden states, and exploits parallel prefix-sum computation for GPU acceleration, achieving $O(\log N)$ time complexity in state updates. Key contributions include a diagonalized, complex-valued state-space parameterization with stability constraint ${\rho}(\Lambda) < 1$ and oscillation bias via $\lambda = e^{-v+i\theta}$, a smooth-evolution loss term, and demonstrated speedups up to $2.2\times$ on long sequences, while delivering RMSE around $1\,K$ on a real PMSM dataset with a compact model (~8k parameters). The approach offers a practical, scalable solution for real-time thermal management and health monitoring in industrial electric machinery, with potential deployment on edge GPUs and embedded devices.

Abstract

Accurate and efficient thermal dynamics models of permanent magnet synchronous motors are vital to efficient thermal management strategies. Physics-informed methods combine model-based and data-driven methods, offering greater flexibility than model-based methods and superior explainability compared to data-driven methods. Nonetheless, there are still challenges in balancing real-time performance, estimation accuracy, and explainability. This paper presents a hardware-efficient complex neural dynamics model achieved through the linear decoupling, diagonalization, and reparameterization of the state-space model, introducing a novel paradigm for the physics-informed method that offers high explainability and accuracy in electric motor temperature estimation tasks. We validate this physics-informed method on an NVIDIA A800 GPU using the JAX machine learning framework, parallel prefix sum algorithm, and Compute Unified Device Architecture (CUDA) platform. We demonstrate its superior estimation accuracy and parallelizable hardware acceleration capabilities through experimental evaluation on a real electric motor.

Figures (10)

• Figure 1: Pipeline of the parallel prefix sum algorithm, where $z_i$ is the input and $s_i$ denotes the $\sum_{j=0}^iz_i$ when the binary operator is plus.
• Figure 2: Structure of the Complex Neural Dynamics Model (complexNDM). Given the PMSM's motor previous temperature measurements to estimate the initial state and parallel compute system outputs by control inputs. The loss function contains a priori bias towards a smooth evolution of non-chaotic systems. Parallel computing is based on the parallel prefix sum algorithm (Scan), which can be implemented in GPUs by CUDA. The complex diagonal parameterization of the state matrix incorporates the physical priori information concerning system stability and low oscillation frequency.
• Figure 3: The average proportion of real and complex values in the eigenvalues of a random square matrix.
• Figure 4: The distribution of randomly generated $\bm{\lambda} \in \mathbb{C}^{32}$ on the complex plane when $r_{min}=0.4$, $r_{max}=0.8$, and $\Phi=\pi/4$. Note that the eigenvalue with a negative imaginary part is the complex conjugate of an eigenvalue with a positive imaginary part.
• Figure 5: The upper figure is the state transition trajectories without system input when $\Phi=\pi$ and the lower figure is the same state transition trajectories without system input when $\Phi=\pi/ 10$.

Theorems & Definitions (2)

• Theorem 1
• Proof 1