Fundamental flaws of physics-informed neural networks and explainability methods in engineering systems

• PINNs embed idealized equations that omit critical multiscale & boundary effects. • XAI methods create explanations based on correlations that violate physics laws. • Multiplicative error propagation creates false confidence in plausible predictions. • Three interconnected failure modes compromise integrity of physics-informed ML. • Engineers face systematic risks from methods that appear reliable but mask flaws. Physics-informed neural networks (PINNs) and explainable artificial intelligence (XAI) have gained widespread adoption for their ability to integrate data-driven modeling with constitutive laws and interpretable predictions. However, despite their success, these methods harbor systematic risks that not only compromise their integrity but also remain largely invisible. Through our review and a series of classical mechanistic case studies, we identify three interconnected failure modes. First, PINNs embed idealized governing equations that often omit critical multiscale phenomena, boundary complexities, and nonlinear couplings. Second, post-hoc explainability methods generate attributions based on statistical correlations that are likely to conflict with causal principles, which can result in producing explanations that violate conservation laws and misrepresent true mechanisms. Third, and most critically, these failures create a multiplicative propagation of errors that, unlike traditional numerical methods with quantifiable errors, produce false confidence through predictions that appear physically plausible while masking critical omissions. Toward the end of this paper, we present engineering-specific consequences of these failure modes and provide recommendations for proper deployment.