AI Models Magnetism with Greater Accuracy and Data Efficiency

Researchers are tackling the challenge of accurately modelling the complex magnetic behaviour of synchronous machines, a crucial step towards improving their control and efficiency. Junyi Li, Tim Foißner, and Floran Martin, all from Aalto University, alongside Antti Piippo from ABB Oy and Marko Hinkkanen from Aalto University, present a novel physics-informed neural network approach that directly incorporates gradient networks into the fundamental equations governing magnetic fields. This collaborative work offers a significant advancement over traditional methods like lookup tables, requiring less training data while ensuring physically realistic and reliable model extrapolation. The resulting models, validated using both measured and finite-element method datasets from a 5.6-kW permanent-magnet synchronous reluctance machine, promise to enable robust model inversion and optimal trajectory generation for advanced control applications.

A novel modelling technique for electric motors promises more efficient and reliable performance. The advance tackles a long-standing challenge in accurately simulating the complex magnetic behaviour within these machines, potentially unlocking improvements in everything from industrial automation to electric vehicle performance. By integrating physics-informed neural networks, researchers have achieved unprecedented accuracy and efficiency in modelling the complex magnetic behaviour within electric machines.

This work addresses a longstanding challenge in electric drive technology, creating dynamic models that accurately capture magnetic saturation and spatial harmonics, crucial for optimal performance and control. The team’s innovation lies in an architecture that directly incorporates the fundamental equations governing electromagnetic fields into the neural network itself, ensuring inherent physical consistency.

By modelling the gradient of magnetic field energy, the system automatically satisfies energy balance principles, a critical requirement for reliable operation and robust control strategies. This new modelling framework transcends the limitations of traditional methods such as lookup tables and standard machine learning techniques. These conventional approaches often demand extensive training datasets, struggle with extrapolation beyond known data, and can produce outputs lacking smoothness.

In contrast, the proposed architecture requires significantly less training data, guarantees monotonicity, a property ensuring predictable behaviour, and generates remarkably smooth outputs. These characteristics unlock the potential for robust model inversion and the generation of optimal trajectories, essential for advanced control applications in electric drives.

The core of this advancement is the use of gradient networks, a specialised type of neural network capable of universally approximating any physically plausible magnetic behaviour. Unlike previous Hamiltonian neural networks which rely on numerical differentiation, this approach directly models conservative vector fields, eliminating a key source of error and improving computational efficiency.

By directly learning the relationships between magnetic flux, currents, and rotor angle, the model accurately represents the complex interplay of forces within the machine. Validation using both measured data and finite-element method simulations from a 5.6-kW permanent-magnet synchronous reluctance machine demonstrates the accuracy and physical consistency of the model, even when trained with limited data.

This research paves the way for more efficient and reliable electric drives, enabling improved performance in a wide range of applications, from electric vehicles to industrial automation. The ability to accurately model complex magnetic behaviour with minimal data opens up new possibilities for real-time control, predictive maintenance, and the design of next-generation electric machines.

Energy conservation and invertible relationships via monotone gradient networks

The proposed physics-informed neural network accurately models a 5.6-kW permanent-magnet synchronous reluctance machine, demonstrating physically consistent behaviour even with limited training data. Crucially, the model inherently satisfies energy balance through the direct implementation of gradient networks, ensuring reciprocity conditions are met without additional constraints.

This is achieved by modelling the stator current and electromagnetic torque as gradients of a scalar field energy function, a fundamental aspect of the research. The architecture universally approximates any physically feasible magnetic behaviour, offering advantages over traditional lookup tables and standard machine learning approaches. Monotone gradient networks were employed to guarantee the convexity of the field energy, establishing a unique and invertible relationship between flux linkages and currents.

This allows for the formulation of both current and flux-linkage maps, enhancing the model’s versatility and robustness. Incorporation of Fourier features successfully captures spatial harmonics while maintaining the lossless, conservative structure of the field, improving accuracy in complex scenarios. The study also explored activation functions, proposing a computationally efficient p-norm gradient activation as an alternative to the more commonly used softmax function.

The model’s ability to accurately represent magnetic saturation and angle dependency is a key achievement, addressing a significant challenge in high-fidelity machine modelling. By directly modelling conservative vector fields, the research avoids the need for numerical differentiation of a scalar neural network, improving both data efficiency and generalisation capability. This approach allows for robust model inversion and optimal trajectory generation, essential components in advanced control applications for electric drives.

Physically Consistent Modelling via Monotone Gradient Networks and Fourier Features

Gradient networks underpin the core of this work, directly modelling conservative vector fields to accurately represent the electromagnetic behaviour of synchronous machines. Rather than relying on conventional neural networks or lookup tables, the research implements an architecture where the stator current and electromagnetic torque are defined as gradients of a scalar field energy function.

This innovative approach intrinsically guarantees physical consistency, specifically energy balance and reciprocity, by design. Monotone gradient networks are employed to ensure the convexity of the field energy, establishing a unique and invertible relationship between flux linkages and currents, crucial for both forward and inverse mapping. To capture the complexities of real-world machines, Fourier features are integrated into the network.

These features allow the model to represent spatial harmonics within the magnetic field while simultaneously preserving the lossless, conservative structure of the energy field. This is a significant methodological advancement, as it avoids the limitations of analytical functions or the memory demands of high-dimensional lookup tables. The chosen architecture universally approximates any physically feasible magnetic behaviour, offering a robust alternative to traditional modelling techniques.

Validation involved utilising both measured datasets and those generated via finite-element method (FEM) simulations from a 5.6-kW permanent-magnet synchronous reluctance machine. This dual approach ensured the model’s accuracy across a range of operating conditions and provided a benchmark against established simulation techniques. The methodology prioritises data efficiency, requiring less training data than conventional machine learning approaches while maintaining a high degree of accuracy and physical plausibility.

Physics-informed neural networks enhance modelling of electrical machine performance and reliability

Scientists have long struggled to create accurate digital twins of complex physical systems, and this work represents a significant step forward in that endeavour. The challenge isn’t replicating behaviour, but doing so in a way that respects the underlying laws of physics. Traditional machine learning models, while adept at pattern recognition, can easily produce unrealistic outputs, particularly when extrapolating beyond their training data.

This new approach, employing physics-informed neural networks, directly embeds those physical constraints into the model itself. The implications extend beyond simply improving the fidelity of simulations. Accurate and efficient modelling is crucial for optimising the performance of electrical machines like synchronous reluctance motors, leading to increased energy efficiency and reduced operating costs.

Crucially, the ability to reliably extrapolate allows for predictive maintenance and the design of more robust control systems, potentially preventing failures before they occur. The reduced need for extensive training data is also a major boon, lowering the barrier to entry for applying these techniques to new and varied systems. However, this isn’t a universal solution.

The current validation focuses on a specific motor size and operating conditions. Scaling this approach to significantly larger or more complex machines will undoubtedly present new challenges. Furthermore, while the model enforces energy balance, it doesn’t address all possible physical constraints, and the choice of which constraints to include remains a critical design decision.

Looking ahead, we can anticipate a broader integration of physics-informed machine learning across various engineering disciplines. The next frontier lies in developing automated methods for identifying and incorporating relevant physical laws, potentially creating self-aware models capable of adapting to unforeseen circumstances. This could unlock a new era of intelligent systems, seamlessly blending the power of data-driven learning with the elegance of fundamental physics.