Alberto Miño Calero

Alberto Miño Calero, Luis Salamanca, Konstantinos E. Tatsis

Physics-Informed Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PINN models remain difficult to train and interpret. In this work, a novel modeling approach is proposed, which relies on the use of Domain-aware Fourier Features (DaFFs) for the positional encoding of the input space. These features encapsulate all the domain-specific characteristics, such as the geometry and boundary conditions, and unlike Random Fourier Features (RFFs), eliminate the need for explicit boundary condition loss terms and loss balancing schemes, while simplifying the optimization process and reducing the computational cost associated with training. We further develop an LRP-based explainability framework tailored to PINNs, enabling the extraction of relevance attribution scores for the input space. It is demonstrated that PINN-DaFFs achieve orders-of-magnitude lower errors and allow faster convergence compared to vanilla PINNs and RFFs-based PINNs. Furthermore, LRP analysis reveals that the proposed leads to more physically consistent feature attributions, while PINN-RFFs and vanilla PINNs display more scattered and less physics-relevant patterns. These results demonstrate that DaFFs not only enhance PINNs' accuracy and efficiency but also improve interpretability, laying the ground for more robust and informative physics-informed learning.

Aleksander Østensen, Alberto Mino Calero, Anastasios M. Lekkas et al.

Large Language Models (LLMs) are increasingly used for decision-making and reasoning tasks, yet their potential as controllers for physical systems remains largely unexplored. This work investigates whether LLMs can function as interpretable controllers for a dynamic thermal environment, examining their ability to follow setpoints, interpret natural-language commands, reason about actuator effects, and incorporate prior model-based knowledge. Five LLMs of varying scales are evaluated under multiple scenarios, including settings with penalties on heater or fan usage and cases where the models have access to a physics-based prediction tool. The results show that control performance depends on model complexity: while low- and mid-scale models frequently misinterpret actuator dynamics or generate inconsistent reasoning, high-complexity models such as Qwen-3~14B and GPT-4o achieve accurate temperature tracking, stable actuator usage, and coherent explanations aligned with physical principles. Incorporating a physics-based model significantly improves control smoothness and energy efficiency by enabling anticipatory decision-making. A detailed reasoning taxonomy further reveals a clear progression from causal misinterpretation in smaller models to cohesive and temporally aware reasoning in larger ones. The findings demonstrate that LLMs can act as interpretable controllers when sufficiently capable and appropriately grounded in domain knowledge, highlighting promising opportunities for hybrid model-based and language-driven control strategies that can provide plausible explanations.