Kalyan S. Perumalla | Searcharxiv

arXiv2026

Porting the Nonlinear Optimization Library HiOp to Accelerator-Based Hardware Architectures

While interior point methods have been the centerpiece of nonlinear programming tools used in science and engineering, their reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it difficult to implement them effectively on hardware accelerators. At this time, there are few sparse linear solvers that can be used in this context. Here, we present a novel formulation of an interior point method implemented in our HiOp library, which is designed to be able to run entirely on hardware accelerators. This formulation avoids dependence on sparse solvers altogether, which is achieved by compressing the underlying sparse linear problem into a dense one of manageable size. We demonstrate feasibility of this approach and provide a baseline for future interior point method implementations on hardware accelerators. Our investigation is motivated by problems arising in optimal power flow analysis in power systems engineering and our approach is tailored to the broad class of problems arising in that important domain. We also demonstrate utility of modern programming models based on performance portability libraries, namely, Umpire and RAJA. We discuss trade-offs between performance, portability and development cost in the solution space for this non-linear optimization problem. As a result of this research, we demonstrate for the first time that interior point methods for sparse problems can be efficiently realized on modern computing systems where more than 90% of processing power is in GPUs.

cs.MS↗

arXiv2013

Reversible Simulations of Elastic Collisions

Consider a system of N identical hard spherical particles moving in a d-dimensional box and undergoing elastic, possibly multi-particle, collisions. We develop a new algorithm that recovers the pre-collision state from the post-collision state of the system, across a series of consecutive collisions, with essentially no memory overhead. The challenge in achieving reversibility for an n-particle collision (where, n << N) arises from the presence of nd-d-1 degrees of freedom during each collision, and from the complex geometrical constraints placed on the colliding particles. To reverse the collisions in a traditional simulation setting, all of the particular realizations of these degrees of freedom during the forward simulation must be saved. This limitation is addressed here by first performing a pseudo-randomization of angles, ensuring determinism in the reverse path for any values of n and d. To address the more difficult problem of geometrical and dynamic constraints, a new approach is developed which correctly samples the constrained phase space. Upon combining the pseudo-randomization with correct phase space sampling, perfect reversibility of collisions is achieved, as illustrated for n <= 3, d=2, and n=2, d=3 (and, in principle, generalizable to larger n). This result enables for the first time reversible simulations of elastic collisions with essentially zero memory accumulation. The reverse computation methodology uncovers important issues of irreversibility in conventional models, and the difficulties encountered in arriving at a reversible model for one of the most basic physical system processes, namely, elastic collisions for hard spheres. Insights and solution methodologies, with regard to accurate phase space coverage with reversible random sampling proposed in this context, can help serve as models and/or starting points for other reversible simulations.

physics.comp-ph↗