Jheng-Wei Li (CEA)
Many problems in science and engineering are described by partial differential equations (PDEs). Examples range from neutron diffusion in nuclear reactors to electron motion on superlattices. These equations are hard to solve in practice because they involve many different length scales that render conventional discretization approaches prohibitively costly.
In this talk, I will show how ideas from many-body physics, in particular tensor networks, can overcome this difficulty. Tensor networks are clever ways of compressing large, structured data without losing essential information. Originally invented to describe quantum many-body wavefunctions, they can also be adapted to PDEs. I will use two simple, instructive examples to illustrate how to accomplish this.
The key message is that “exponentially many” variables do not necessarily imply “exponentially hard” computations. By bridging concepts from many-body physics and functions of continuous variables, tensor networks give a promising pathway toward a scalable approach for multi-scale PDEs and beyond.
Contact : S. Capponi