Tensor Neural Network PDE Solver - ON-1193
Genre de projet: RechercheDiscipline(s) souhaitée(s): Génie - informatique / électrique, Génie
Entreprise: Multiverse Computing
Durée du projet: Plus d’un an
Date souhaitée de début: Dès que possible
Langue exigée: Anglais
Emplacement(s): Toronto, ON, Canada
Nombre de postes: 1
Niveau de scolarité désiré: MaîtriseDoctoratRecherche postdoctorale
Ouvert aux candidatures de personnes inscrites à un établissement à l’extérieur du Canada: No
Au sujet de l’entreprise:
Multiverse is a well funded deep-tech Canadian company. We are one of the few world companies working with Quantum Computing.
We provide hyper-efficient software for companies from the financial industry wanting to gain an edge with quantum computing and artificial intelligence. Our main verticals are fraud detection, credit scoring assessment, and financial optimization.
Our team of experts is world-renowned for innovative approaches to intractable financial and macro-economics problems. We work with quantum hardware and quantum inspired methods to build machine learning solutions which exceed the predictive power of the current best solutions.
We are applying to Mitacs to allow us to expand our R&D team in Canada to tackle problems of huge commercial impact and expand our expertise.
Veuillez décrire le projet.:
(1) Build a full literature review documenting methods to accelerate neural network training using tensor networks, (2) Map PDEs of industrial relevance, such as the Navier Stokes equation and the Black Scholes model, to stochastic DEs in view of solving them using tensor neural networks, (3) Build a full and comprehensive benchmark of the PDE solver on these equations, (4) Compare the performance with classical neural networks, finite difference methods, and standard Monte Carlo methods.
Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. These equations are often solved using finite difference or Monte Carlo methods, which is often computationally expensive. Recent advances in deep learning have shown we can solve high dimensional PDEs in a high dimension – thereby addressing the curse – using neural networks [arXiv:1804.07010]. This raises a new challenge: training these models, which is computationally intensive. We aim to tackle these shortcomings by replacing some of the dense layers within the neural network by Tensor Networks layers. This quantum-inspired neural network architecture – or Tensor Neural Network (TNN) – has shown it can significantly accelerate training and make better use of memory [arXiv:1506.08473]. Part of the founding team of Multiverse Computing are credited with significantly advancing the field of tensor networks [DOI:10.1016/j.aop.2014.06.013]. We will leverage this expertise to expand on the bleeding edge of deep learning. The output of this project will be a Tensor Neural Network capable of tackling a wide variety of parabolic PDEs.
Expertise ou compétences exigées:
Understand the basics of tensor network for machine learning.
Develop ideas for designing ODE and PDE solver with tensor network.
Strong understanding of neural networks for fitting quasilinear partial differential equations.
