Experimental observation on a low-rank tensor model for eigenvalue problems
This work addresses eigenvalue problems in computational physics, but it appears incremental as it compares variants of existing low-rank tensor methods.
The authors tackled eigenvalue problems for the Laplacian operator and harmonic oscillator using a low-rank tensor model with gradient descent, showing that a polynomial-based variant outperformed a tensor neural network in experiments.
Here we utilize a low-rank tensor model (LTM) as a function approximator, combined with the gradient descent method, to solve eigenvalue problems including the Laplacian operator and the harmonic oscillator. Experimental results show the superiority of the polynomial-based low-rank tensor model (PLTM) compared to the tensor neural network (TNN). We also test such low-rank architectures for the classification problem on the MNIST dataset.