Physics‐informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have shown that when designing loss functions for many engineering problems, using first‐order derivatives and combining equations from both strong and weak forms can lead to much better accuracy, especially when there are heterogeneity and variable jumps in the domain. This new approach is called the mixed formulation for PINNs, which takes ideas from the mixed finite element method. In this method, the PDE is reformulated as a system of equations where the primary unknowns are the fluxes or gradients of the solution, and the secondary unknowns are the solution itself. In this work, we propose applying the mixed formulation to solve multi‐physical problems, specifically a stationary thermo‐mechanically coupled system of equations. Additionally, we discuss both sequential and fully coupled unsupervised training and compare their accuracy and computational cost. To improve the accuracy of the network, we incorporate hard boundary constraints to ensure valid predictions. We then investigate how different optimizers and architectures affect accuracy and efficiency. Finally, we introduce a simple approach for parametric learning that is similar to transfer learning. This approach combines data and physics to address the limitations of PINNs regarding computational cost and improves the network's ability to predict the response of the system for unseen cases. The outcomes of this work will be useful for many other engineering applications where deep learning is employed on multiple coupled systems of equations for fast and reliable computations.

Summary: The realistic representation of material degradation at a fully evolved crack is still one of the main challenges of the phase‐field method for fracture. An approach with realistic degradation behavior is only available for isotropic elasticity in the small deformation framework. In this paper, a variational framework is presented for the standard phase‐field formulation, which allows to derive the kinematically consistent material degradation. For this purpose, the concept of representative crack elements (RCE) is introduced to analyze the fully degraded material state. The realistic material degradation is further tested using the self‐consistency condition, where the behavior of the phase‐field model is compared to a discrete crack model. The framework is applied to isotropic elasticity, anisotropic elasticity and thermo‐elasticity, but not restricted to these constitutive formulations.