PINNA: Physics‐Informed Neural Networks Architecture for Implicit Governing Physics With Interpretability

Abstract

Modern engineering simulations frequently operate in regimes where explicit governing equations are incomplete or experiments are prohibitively expensive. To remain accurate and trustworthy under such constraints, we propose the Physics‐Informed Neural Network Architecture (PINNA) , a deep‐learning surrogate that fuses data with domain knowledge inside the network. Concretely, a fully connected encoder embeds raw inputs (e.g., material descriptors, loads, or operating conditions) into a latent space, while an intermediate‐physics head is explicitly supervised to predict expert‐selected quantities with clear physical meaning, such as strain‐energy densities or chemically relevant indicators. These intermediate predictions are residual‐concatenated with the original inputs and passed to a task decoder , enabling the network to learn and correct mismatches between approximate physics and observed responses. This architecture achieves (i) higher accuracy and sample efficiency than purely data‐driven baselines, (ii) negligible computational overhead at inference time, and (iii) intrinsic interpretability , as intermediate predictions expose physically meaningful internal representations. We further introduce a scalable extension, Generalized PINNA ( G‐PINNA ), which stacks multiple physics heads to accommodate multiscale and multi‐physics constraints within the same residual‐concatenation framework. PINNA is validated across three fundamentally different benchmarks: two composite‐material problems involving nonlinear stress‐strain behavior and multistage failure, and a large‐scale 1‐D laminar combustion problem governed by stiff chemical kinetics, thermal transport, and reduced fluid mechanics. In the composite benchmarks, PINNA reduces test errors by up to an order of magnitude relative to Fourier Neural Operators and DeepONets while using fewer parameters. In the combustion benchmark, PINNA accurately predicts both interpretable intermediate chemical indicators and high‐dimensional flame quantities, including scalar metrics and full spatial profiles, demonstrating that intermediate supervision enables robust generalization beyond solid mechanics. These results confirm that embedding expert knowledge directly into neural architectures provides a practical, interpretable, and general framework for learning implicit physics across diverse engineering domains.