International Conference on Computer and Knowledge Engineering

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TD-PINNs: Efficient Shared-Memory Parallelization of Physics-Informed Neural Networks for Time-Dependent PDEs

Authors :

Mahdi Movahedian Moghaddam¹ Kourosh Parand²

1- Department of Computer and Data Sciences, Shahid Beheshti University 2- Department of Computer and Data Sciences, Shahid Beheshti University

Keywords :

Strong-Form PINNs،Temporal Basis Decomposition،High-dimensional PDEs

Abstract :

We present a parallel framework for solving time-dependent partial differential equations (PDEs) using Temporally-Decomposed Physics-Informed Neural Networks (TD-PINNs). In this architecture, the solution is expressed as a sum of temporal basis functions, each modulating an independent spatial neural subnetwork. This decomposition naturally enables parallelism by assigning separate CPU threads to different subnetworks. Unlike traditional PINNs, our method avoids global network coupling and monolithic training, significantly improving scalability. We implement a shared-memory parallel training strategy in PyTorch using thread-level concurrency and show that TD-PINNs achieve up to 2.29× speed-up on multicore CPUs without sacrificing accuracy. Experiments on both linear (heat) and nonlinear (viscous Burgers) PDEs demonstrate stable convergence and improved runtime, especially in nonlinear regimes. Compared to spatial decomposition strategies like XPINNs, TD-PINNs offer simpler implementation, lower overhead, and better speed-up under shared-memory systems. Our results highlight TD-PINNs as a lightweight, parallel-ready alternative to standard PINNs, well-suited for CPU-based scientific computing with minimal architectural modifications.