MICDE – Mechanical Engineering seminar: Phani Motamarri, Indian Institute of Science, Bangalore

Talk title: Inexact yet Accurate: Unlocking Quantum Modeling of Materials at Scale through Approximation-Tolerant Algorithms Abstract: Modern computing architectures increasingly rely on iterative solvers that employ reduced-precision computation and communication-reduction techniques to lower time-to-solution and improve scalability. However, eigensolvers in scientific simulations have struggled to exploit such approximations without compromising accuracy. We present an eigensolver R-ChFSI, a residual-based reformulation of Chebyshev Filtered Subspace Iteration (ChFSI) provably tolerant to inexact matrix–vector products. By expressing the Chebyshev recurrence in terms of residuals rather than eigenvector estimates, R-ChFSI naturally accommodates multiple sources of approximation, including reduced-precision arithmetic (FP32 and TF32) in the filtering step, lossy compression with compression ratios exceeding 4x for inter-process communication, and approximate inverses for generalized eigenproblems, while preserving eigensolver robustness. Large-scale experiments on GPU accelerators are conducted using finite-element discretized generalized eigenproblems arising in Kohn–Sham density functional theory for quantum modeling of materials. The results demonstrate that R-ChFSI achieves eigen-residual norms orders of magnitude smaller than standard ChFSI under comparable inexactness, while delivering substantial performance gains. This work provides a practical pathway toward approximation-tolerant eigensolvers enabling accurate and scalable simulations on modern computing architectures.