Physical Reservoir Computing with Nonlinear Temperature Characteristics of Thermal Conductivity

Abstract

Physical reservoir computing (PRC) has emerged as a low-cost machine-learning framework for edge computing applications, where real-time processing and energy efficiency are critical due to the rapid growth of data generated by Internet-of-Things devices. This study proposes a PRC scheme based on nonlinear heat-conduction phenomena arising from the nonlinear temperature-dependent thermal conductivity of materials and examines its computational properties using a one-dimensional model. Information is encoded as transient thermal inputs applied at one boundary, while the resulting temporal temperature responses at multiple spatial positions constitute the reservoir states. Nondimensionalization of the governing heat equation reveals key dimensionless parameters that govern dynamical memory and nonlinearity, enabling systematic exploration of the design space independent of specific physical units. Performance is evaluated using benchmark tasks, including the short-term memory (STM) task and the parity check (PC) task. The results demonstrate that memory capacity and nonlinear transformation capability can be tuned by adjusting the heat-input magnitude and the thermal diffusion time scale. The proposed heat-conduction-based PRC successfully performs both benchmark tasks, demonstrating the feasibility of implementing PRC through nonlinear thermal transport in materials with temperature-dependent thermal conductivity. These findings indicate that engineered thermal media can serve as effective physical reservoirs with material-level tunability for energy-efficient computing systems.