Thermal hardware software co-design controls microprocessor heat safely
ADACT: PDE-Constrained Thermal Hardware/Software Co-Design Adjoint-Driven Optimal Control via Finite Difference Discretization
Hardware Architecture
Summary
Modern computer chips run hot because they do a lot of work in a small space, which can cause them to slow down or get damaged. This paper presents ADACT, a method that helps manage chip temperature by controlling both the hardware (cooling systems) and software (workload) together in a smart way. The method uses accurate mathematical models of heat flow and an efficient way to calculate how to adjust system components to keep the chip cool without slowing it down too much. The authors test their method using simulations and confirm it works well to keep temperatures safe while maintaining performance.
What this means in practice
- •For chip designers: Design thermal management systems that jointly optimize cooling hardware and workload to prevent overheating while preserving chip performance.
- •For data center operators: Implement smarter dynamic thermal controls that adjust cooling and computing load to reduce energy use and maintain safe operation of server processors.
Authors
Don Li
Abstract
By virtue of the sheer compute demands of large-scale artificial intelligence (AI) and high-performance computing (HPC), modern multi-core microprocessors suffer from severe power density limits and thermal throttling, entailing an urgent need for principled methods for predictive, physics-informed dynamical thermal management (DTM). Here, we introduce a hardware/software co-design physics-informed PDE-constrained DTM throttling optimal control algorithm, ADACT (Adjoint-Driven Adaptive Co-Design Thermal Control), that minimizes thermal risk and cooling energy overhead while maximizing core execution throughput. The underlying physical temperature field is governed by a two-dimensional nonhomogeneous parabolic reaction-diffusion equation with spatially localized, time-varying power source terms and variable convective cooling subject to nonhomogeneous Dirichlet boundary conditions. We employ a discretization of the continuous state PDE via a Crank-Nicolson finite difference scheme with a 5-point discrete Laplacian operator on a uniform spatial mesh, which preserves unconditional numerical stability and $O(Δx^2 + Δy^2 + Δt^2)$ second-order temporal and spatial accuracy. To efficiently compute exact gradients, we construct and implement a continuous backward-in-time adjoint state method with L-BFGS as our optimization algorithm of choice. The accuracy and second-order convergence rates of both forward state and backward adjoint solvers are quantitatively verified via the Method of Manufactured Solutions (MMS), and gradient accuracy is validated using directional derivative Taylor tests. Numerical experiments demonstrate that ADACT dynamically throttles software power workloads and modulates hardware cooling efforts to strictly uphold physical thermal thresholds while maintaining operational throughput.