This research will develop new mathematical and computational tools that can significantly improve the speed, reliability, and realism of scientific simulations across a broad range of scientific and engineering applications. These capabilities are expected to support data-driven computational methods and AI-assisted engineering design and scientific discovery by enabling high-fidelity predictive models that reliably capture wave propagation, transport, and multiscale physical interactions, as well as producing simulation data that is sufficiently accurate and robust to serve as a foundation for training, validating, and benchmarking next-generation AI-based methods. The work is also relevant to wave and quantum phenomena arising in emerging sensing, photonic, and quantum-device technologies. Potential biomedical applications include improved computational approaches for medical imaging, ultrasound, diffusion and transport in biological systems, and related health technologies that depend on accurate wave and transport simulations. In manufacturing and materials engineering, the resulting methods may contribute to the design and optimization of next-generation materials, microelectronic and photonic components, and precision production processes requiring accurate modeling of complex geometries and wave interactions. Broadly, the project will provide foundational capabilities that enable faster innovation, improved predictive technologies, and efficient use of high-performanc