Glossary

Physics-Informed Neural Network (PINN)

A deep learning model that integrates the governing thermodynamic differential equations of transformer heat transfer directly into the loss function to constrain predictions to physical reality.

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SCIENTIFIC MACHINE LEARNING

What is Physics-Informed Neural Network (PINN)?

A deep learning framework that embeds physical laws directly into the neural network training process to ensure predictions are consistent with established scientific principles.

A Physics-Informed Neural Network (PINN) is a deep learning model that integrates governing physical equations—typically partial differential equations (PDEs)—directly into its loss function as a regularization constraint. Unlike purely data-driven models, a PINN penalizes solutions that violate known physics, forcing the network to learn representations that satisfy conservation laws, boundary conditions, and initial conditions even in regions with sparse or noisy observational data.

In transformer predictive maintenance, PINNs encode the thermodynamic heat transfer equations governing winding hot-spot temperature evolution and oil convection dynamics. By constraining predictions to obey Fourier's law of heat conduction and fluid dynamics principles, the model generates physically plausible thermal forecasts that prevent nonsensical extrapolations, enabling reliable remaining useful life (RUL) estimation even when training data is limited to normal operating regimes.

PHYSICS-INFORMED NEURAL NETWORKS

Key Characteristics of PINNs

Physics-Informed Neural Networks (PINNs) fundamentally differ from conventional deep learning by embedding governing physical laws directly into the training process. This ensures predictions are not just data-driven but also thermodynamically and physically consistent.

Governing Equation Embedding

The defining feature of a PINN is the integration of partial differential equations (PDEs) into the neural network's loss function. For transformer thermal modeling, this means embedding the heat transfer equation and IEEE C57.91 loading guide constraints. The network is penalized not only for mismatching sensor data but also for violating the conservation of energy, forcing predictions to remain physically plausible even when extrapolating beyond training data.

Data-Physics Hybrid Loss Function

The total loss function is a weighted sum of multiple components:

Data Loss: Mean squared error between predicted and measured top-oil or hot-spot temperatures.
Physics Loss: Residual of the governing PDE evaluated at collocation points throughout the domain.
Boundary/Initial Loss: Constraints enforcing known ambient temperature conditions and initial thermal states. This hybrid approach allows the model to learn from sparse sensor data while being regularized by physical law.

Mesh-Free Discretization

Unlike traditional Finite Element Method (FEM) or Computational Fluid Dynamics (CFD) solvers, PINNs do not require a predefined computational mesh. Collocation points are sampled randomly or adaptively throughout the spatial-temporal domain. This mesh-free nature makes PINNs highly suitable for inverse problems in transformer diagnostics, such as identifying the location and intensity of an internal heat source from surface temperature measurements.

Inverse Problem Solving

PINNs excel at inverse modeling, where unknown parameters of the governing equations are treated as trainable variables. In a transformer context, this allows the network to simultaneously:

Reconstruct the internal temperature field.
Infer unmeasured physical properties like thermal conductivity degradation or cooling oil viscosity changes.
Quantify the severity of a winding hotspot from limited external sensor data. This capability directly supports Remaining Useful Life (RUL) estimation.

Automatic Differentiation for Gradients

PINNs leverage the automatic differentiation (AD) engine built into deep learning frameworks like TensorFlow or PyTorch. AD computes exact derivatives of the network output with respect to its spatial and temporal inputs. These derivatives are substituted directly into the governing PDE residual, avoiding the numerical approximation errors inherent in traditional finite difference methods. This provides high-fidelity gradient fields for thermal flux analysis.

Continuous-Time Prediction

A single trained PINN acts as a continuous function approximator over the entire input domain, not just at discrete time steps. Once trained, the model can be queried at any arbitrary time instant to predict the hot-spot temperature trajectory. This enables smooth interpolation between SCADA sampling intervals and allows for high-resolution forecasting of thermal runaway conditions without the need for sequential autoregressive rollouts.

PHYSICS-INFORMED NEURAL NETWORKS

Frequently Asked Questions

Explore the core concepts behind Physics-Informed Neural Networks (PINNs) and their application in enforcing thermodynamic laws within transformer predictive maintenance models.

A Physics-Informed Neural Network (PINN) is a deep learning framework that integrates governing physical laws—typically expressed as partial differential equations (PDEs)—directly into the loss function of a neural network. Unlike purely data-driven models that rely solely on observational data, a PINN penalizes predictions that violate known physics, such as the heat transfer equation or Navier-Stokes equations. This is achieved by adding a physics-based residual term to the standard data loss. During training, the network uses automatic differentiation to compute the derivatives required by the PDE, constraining the solution space to physically plausible outcomes. This hybrid approach allows PINNs to generalize effectively even with sparse or noisy sensor data, making them ideal for solving forward and inverse problems in complex engineering systems like transformer thermal dynamics.

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About the author

Prasad Kumkar

CEO & MD, Inference Systems

Prasad Kumkar is the CEO & MD of Inference Systems and writes about AI systems architecture, LLM infrastructure, model serving, evaluation, and production deployment. Over 5+ years, he has worked across computer vision models, L5 autonomous vehicle systems, and LLM research, with a focus on taking complex AI ideas into real-world engineering systems.

His work and writing cover AI systems, large language models, AI agents, multimodal systems, autonomous systems, inference optimization, RAG, evaluation, and production AI engineering.

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Physics-Informed Neural Network (PINN)

What is Physics-Informed Neural Network (PINN)?