Physics-based simulations underpin modern engineering and scientific discovery, enabling high-fidelity modeling of complex systems across aerospace, energy, materials science, climate modeling, and biomedical engineering. These simulations, often governed by partial differential equations and multi-physics coupling, provide accurate representations of real-world phenomena but are computationally intensive, time-consuming, and costly to scale. As design cycles shorten and real-time decision-making becomes essential, traditional numerical solvers such as finite element, finite volume, and computational fluid dynamics frameworks face limitations in high-dimensional optimization, uncertainty quantification, and digital twin deployment. Machine learning surrogate models have emerged as a transformative alternative, approximating the input–output behavior of physics simulations with significantly reduced computational cost. By learning mappings from simulation data, surrogate models such as Gaussian processes, neural networks, physics-informed neural networks, and operator learning frameworks can replicate simulation outputs in milliseconds once trained. These models enable rapid parameter sweeps, real-time control, sensitivity analysis, and design optimization while preserving acceptable accuracy. Hybrid approaches further integrate domain knowledge, enforcing physical constraints to enhance generalization and stability. This paper examines the theoretical foundations, architectural paradigms, performance trade-offs, and validation strategies for machine learning surrogate models replacing conventional physics simulations. It highlights practical implementation considerations, robustness challenges, and governance implications, emphasizing their role in accelerating innovation across computationally demanding scientific and industrial domains.