Aalborg and Porto Researchers Model PDEs With Tensor Networks

Researchers at the Department of Electronic Systems, Aalborg University, Aalborg, Denmark and the University of Porto, Porto, Portugal are applying concepts from quantum physics to model systems governed by advection, diffusion, reaction (ADR) partial differential equations. The team encoded solutions to these equations as matrix product states, representing differential operators as matrix product operators, a framework for tackling these challenging problems. Time integration is performed entirely within this tensor network structure using explicit Euler updates with controlled truncation. Numerical results demonstrate the method remains compact, stable, and accurate across a range of scenarios, capturing both local solution profiles and global observables while…