The advent of exascale computing and the proliferation of artificial intelligence techniques are transforming the landscape of multi-physics simulations. These developments enable the study of complex multi-physics problems with unprecedented fidelity and efficiency. But they also motivate new simulation methodologies to achieve these results. Heterogeneous architectures with throughput-optimized GPUs, for example, scale best with higher-order methods and matrix-free solvers for systems of partial differential equations. Computationally expensive simulations can now be used in optimization problems through coupling with automatic differentiation techniques or creating surrogate AI models. This talk will explore various numerical methods and applications of multi-physics simulations, ranging from dark matter cosmology to modeling turbulence to nuclear fusion. It will also discuss challenges and opportunities associated with harnessing exascale computing and AI techniques in these domains. Ultimately, this talk aims to provide insights into the transformative potential of integrating exascale computing and AI in advancing multi-physics simulations, paving the way for breakthroughs in scientific understanding and technological innovation

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