[Thesis Defense] Performance Portable Scientific Computing through Multi-Level Compiler Optimizations

Scientific computing faces a trade-off between mathematical expressiveness and performance across heterogeneous hardware. This work presents a compiler-driven approach that automatically preserves and recovers mathematical structure in existing scientific codes to generate optimized code without manual re-engineering. By combining graph optimizations, abstraction raising, communication optimizations, multi-level automatic differentiation, and learned cost models within a unified compiler infrastructure, the system enables optimizations that are infeasible in isolation. Our evaluations on large-scale scientific applications, including differentiable climate and hypersonic flow simulations, demonstrate consistent performance gains across thousands of GPUs and TPUs. The methods and artifacts presented in this thesis demonstrate a path toward scientific computing where the complexity of heterogeneous execution is handled automatically, leaving scientists free to focus on the mathematics.