Inventors: Tamer Zaki and Yifan Du
Unmet Need:
Accurate and fast computational solutions of partial differential equations (PDEs) are critical to predictive simulations across physics and engineering subdisciplines. However, PDEs are notoriously difficult to solve, especially in complex systems that involve nonlinear effects, amplification of uncertainties and chaos. Recent machine-learning approaches, including physics informed neural networks (PINNs), attempt to minimize the PDE residuals at randomly generated points across the space-time domain. However, this approach is inefficient and not predictive because it relies on training/optimization over a finite time horizon. Therefore, there is a need for modified techniques to enhance the accuracy and speed of PDE solutions, and enable predictive simulations for any time horizon.
Technology Overview:
Johns Hopkins inventors have developed an evolutionary deep neural network (EDNN, pronounced “Eden”), a novel framework for solving time dependent PDEs. For any initial state of the system, the network parameters are evolved, or updated, deterministically using the governing equations to predict the evolution of the system. EDNN is therefore an AI/ML nonlinear version of finite-element methods, and can accurately and efficiently solve any PDE over indefinitely long time horizons, deterministically and without training.
Stage of Development:
Demonstration ready.
Patent:
Provisional Application filed
Publication:
Y. Du & T.A. Zaki, Evolutional deep neural network, Phys. Rev. E 104, 045303 (2021)
DOI: 10.1103/PhysRevE.104.045303
Available on arXiv (link)
