Thermal energy systems power everything from power generation to manufacturing. Yet accurate prediction under nonlinear, coupled, and geometry-heavy conditions remains stubbornly hard. Conventional simulation strategies may be accurate only within narrow ranges and often struggle when system configurations change or when measurements are sparse and noisy.

The review, published in ENGINEERING Energy, provides a structured taxonomy for applying PINN-DT to industrial thermal challenges. Authored by Sadegh Ataee and Mehran Ameri from Shahid Bahonar University of Kerman, the work synthesizes how physics-informed learning can be combined with digital-physical synchronization rather than treating AI as a standalone black box.

A central contribution is tackling ill-posed thermal problems. PINN-DT can learn solutions for strongly nonlinear heat and flow behaviors that conventional computational methods find inaccessible, improving stability when data is limited.

Another breakthrough is interpretability. By embedding fundamental constraints—such as energy conservation and fluid-dynamical relationships—directly into the training loss, the models remain physically consistent even when observations are incomplete.

Crucially for industry, the review connects predictive modeling to control. When PINN-DT is paired with Model Predictive Control (MPC), the digital twin can forecast future states, enforce operational constraints, and return optimized control signals in real time.

The most notable gap the authors address is exergy. They propose a novel physics-informed loss function derived from exergy analysis, combining the first and second laws of thermodynamics. This exergy-informed formulation is designed to improve predictive accuracy and reduce mismatch between learned dynamics and thermodynamic reality.

The framework is also presented as scalable across sectors, including supercritical CO₂ Brayton cycles, smart power grids, food processing refrigeration, and dynamic HVAC control for GPU-centric data centers.

“The development of robust physics-informed machine learning frameworks fundamentally depends on embedding appropriate physical principles through carefully designed constraint terms,” the authors emphasize, highlighting that loss-function design is not a detail—it is the engine of reliability.

With exergy-guided constraints and MPC-ready digital twins, the review sketches a roadmap for Industry 4.0 systems that minimize energy consumption while maximizing output—delivering viral, near-real-time optimization rather than slow, offline prediction.

Subject of Research: Physics-informed neural network-based digital twins for thermal energy systems (solvability and loss function design)
Article Title: Physics-informed neural network-based digital twins for thermal energy systems: A review of solvability and loss function design
News Publication Date: 10-Jun-2026
Web References: https://doi.org/10.1007/s11708-026-1049-1
References: Ataee, S., Ameri, M. Physics-informed neural network-based digital twins for thermal energy systems: A review of solvability and loss function design. ENG. Energy 20, 10491 (2026).
Image Credits: Sadegh Ataee & Mehran Ameri.

Keywords

Energy, digital twins, physics-informed neural networks, PINN-DT, thermal energy systems, exergy, model predictive control, MPC, thermodynamics