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The integration of physical principles into machine learning (ML) frameworks has emerged as a transformative approach in materials science, addressing the limitations of purely data-driven models by incorporating domain knowledge to enhance predictive accuracy, generalizability, and interpretability. This narrative review explores the conceptual taxonomies of physics-integrated ML methods, their applications in materials discovery and design, and the associated challenges in data bias and ethical considerations. Drawing on recent peer-reviewed literature, we classify physics-integration strategies such as physics-informed neural networks (PINNs), hybrid models combining ML with physical simulations, and constraint-based learning, and highlight their roles in solving complex problems such as material property prediction, microstructure analysis, and phase stability. We also examine how data biases in training datasets can propagate errors and inequities in model outputs, and discuss the ethical values underpinning the use of AI in scientific research, including transparency, accountability, and societal impact. The review underscores the potential of these methods to accelerate innovation in materials science while emphasizing the need for rigorous validation and interdisciplinary collaboration. By synthesizing current advancements, this article aims to provide a foundational understanding for researchers and practitioners, paving the way for future developments in this interdisciplinary field.

In the evolving landscape of computational materials engineering, the integration of multimodal data sources with physics-informed machine learning paradigms promises to revolutionize the pace and precision of materials design and discovery. This conceptual manuscript explores the synergies between diverse data modalities—ranging from experimental spectra to simulation-derived properties—and machine learning models constrained by physical laws, aiming to address persistent challenges in data scarcity, model generalizability, and discovery efficiency within materials science. By synthesizing recent advancements in representation learning, graph neural networks, and autonomous systems, we identify a conceptual gap in holistic frameworks that unify multimodal inputs with physics-based priors for accelerated inverse design. We introduce a novel conceptual framework, termed the Multimodal Physics-Constrained Discovery Engine (MPCDE), which structures data-model-discovery pipelines through layered interactions, feedback mechanisms, and epistemic steering logics. This framework emphasizes computational workflows that balance representation fidelity with inference robustness, incorporating uncertainty quantification to mitigate risks in high-throughput settings. Implications for the field include enhanced coupling of simulation and experimentation, improved scalability of foundation models, and streamlined closed-loop discovery systems. Ultimately, this work posits interpretive insights into how such integrated approaches can transform materials informatics into a more predictive and autonomous discipline, fostering innovations in energy, electronics, and structural materials.